Exhibit 99.1

FOR IMMEDIATE RELEASE

Cole Credit Property Trust III, Inc. Confirms Receipt of Second Revised

Unsolicited Proposal from American Realty Capital Properties, Inc.

PHOENIX, AZ – April 3, 2013 – Cole Credit Property Trust III, Inc. (“CCPT III”) confirmed receipt of a second revised unsolicited proposal on April 2, 2013 (the “second revised proposal”) from American Realty Capital Properties, Inc. (NASDAQ: ARCP), to acquire 100% of the outstanding common stock of CCPT III.

As previously announced, the Special Committee of CCPT III’s Board of Directors, consistent with its fiduciary duties and in consultation with its advisors, is reviewing ARCP’s revised proposal submitted on March 27, 2013. As part of this review, the Special Committee will now also consider the second revised proposal and pursue the course of action that it believes is in the best interests of CCPT III and its stockholders. The Special Committee reiterated that it remains committed to its previously announced course of action to acquire Cole Holdings Corporation.

The Special Committee is disappointed that it must once again set the record straight with respect to ARCP’s assertion that ARCP was unable to engage or communicate with CCPT III’s Special Committee and its advisors. CCPT III noted that the Chairman of its Special Committee, as a representative of the Special Committee, personally held a lengthy conference call with ARCP’s Chairman on Friday, March 29, 2013. The Special Committee’s financial advisors spoke with ARCP’s advisors at length following that call, and again with ARCP and its advisors on Easter Sunday, March 31, 2013, and with ARCP’s advisors three times on Monday, April 1, 2013, in addition to a number of prior conversations and communications. The Special Committee’s legal counsel also had a discussion with ARCP’s counsel about the March 27 proposal.

Goldman, Sachs & Co. and Lazard serve as financial advisors, and Wachtell, Lipton, Rosen & Katz and Venable LLP serve as legal advisors to the Special Committee of the Board of Directors of CCPT III. Morris, Manning & Martin, LLP serves as legal advisor to CCPT III.

About Cole Credit Property Trust III, Inc.

Cole Credit Property Trust III, Inc. is a real estate investment trust that owns and operates a diversified portfolio of core commercial real estate investments primarily consisting of approximately 1,000 necessity retail, office and industrial properties located throughout the United States. CCPT III’s portfolio comprises more than 40 million square feet of rentable space located in 47 states, including properties owned through consolidated joint venture arrangements. As of December 31, 2012, the rentable space at these properties was 99% leased. Since commencement of material operations in January 2009, CCPT III has been externally managed by affiliates of Cole Holdings Corporation.

Additional Information and Where to Find It

This release may be deemed to be solicitation material in respect of the charter amendments to be presented to CCPT III’s stockholders for consideration at the 2013 annual stockholders’ meeting of CCPT III. CCPT III filed a preliminary proxy statement with the SEC and expects to file a definitive proxy statement with the SEC. STOCKHOLDERS ARE URGED TO READ THE DEFINITIVE PROXY STATEMENT AND ANY OTHER RELEVANT DOCUMENTS FILED WITH THE SEC WHEN THEY BECOME AVAILABLE BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION. Stockholders will be able to receive the definitive proxy statement and other relevant documents free of charge at the SEC’s web site at www.sec.gov or by directing a written request to CCPT III at 2325 East Camelback Road, Suite 1100, Phoenix, Arizona 85016, Attention: Investor Relations.

A copy of the merger agreement regarding CCPT III’s acquisition of Cole Holdings has been filed as an exhibit to a Form 8-K CCPT III filed with the SEC on March 8, 2013. The description of the merger agreement contained in this release does not purport to be complete and is qualified in its entirety by reference to the full text of the merger agreement.

Forward-Looking Statements

Certain statements contained in this release may be considered forward-looking statements within the meaning of Section 27A of the Securities Act of 1933, as amended (the “Securities Act”), and Section 21E of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), including statements regarding the CCPT III – Cole Holdings transaction and the ability to consummate the transaction. We intend for all such forward-looking statements to be covered by the safe harbor provisions for forward-looking statements contained in Section 27A of the Securities Act and Section 21E of the Exchange Act, as applicable. Such statements include, in particular, statements about CCPT III’s plans, strategies, and prospects and are subject to certain risks and uncertainties, as well as known and unknown risks, which could cause actual results to differ materially from those projected or anticipated. Therefore, such statements are not intended to be a guarantee of CCPT III’s performance in future periods. Such forward-looking statements can generally be identified by our use of forward-looking terminology such as “may,” “will,” “would,” “could,” “should,” “expect,” “intend,” “anticipate,” “estimate,” “believe,” “continue,” or other similar words. Readers are cautioned not to place undue reliance on these forward-looking statements, which speak only as of the date of this release. CCPT III makes no representation or warranty (express or implied) about the accuracy of any such forward-looking statements contained in this release, and does not intend, and undertakes no obligation, to publicly update or revise any forward-looking statements, whether as a result of new information, future events, or otherwise.

Participants in Solicitation

CCPT III and its directors and executive officers and other members of management may be deemed to be participants in the solicitation of proxies in respect of the charter amendments to be considered at the 2013 annual stockholders’ meeting of CCPT III. Information regarding the interests of CCPT III’s directors and executive officers in the proxy solicitation will be included in CCPT III’s definitive proxy statement.

Contacts

Joele Frank / Meaghan Repko / Nick Lamplough

Joele Frank, Wilkinson Brimmer Katcher

(212) 355-4449