<PAGE>
 
                                                                      EXHIBIT 13

SHAREHOLDER INFORMATION

[LOGO OF COX COMMUNICATIONS APPEARS HERE]

CORPORATE HEADQUARTERS:
Cox Communications, Inc.
1400 Lake Hearn Dr., NE
Atlanta, GA 30319
404-843-5000
www.cox.com

STOCK DATA:
Cox's Class A Common Stock is traded on the New York Exchange.
Ticker symbol: COX.
Daily newspaper stock table listing: CoxComm A.

As of February, 17, 1998, there were 5,585 shareholders of record of Cox's Class
A Common Stock and two shareholders of record of the Class C Common Stock. There
is no established trading market for Cox's Class C Common Stock. There have been
no stock dividends paid on any of Cox's equity securities. Cox does not intend
to pay cash dividends in the foreseeable future. See "Management's Discussion
and Analysis - Liquidity and Capital Resources - Uses of Cash," in the company's
Form 10-K.

QUARTERLY MARKET INFORMATION:

<TABLE>
<CAPTION>
               CLASS A COMMON STOCK          HIGH                  LOW
 
             1997
             <S>                        <C>                  <C>
             First Quarter                     $ 23 1/4             $  19 5/8  
             Second Quarter                      27 7/8                18 1/8  
             Third Quarter                       28 3/16               24 15/16
             Fourth Quarter                      40 1/16               27 11/16 
 
             1996   
             First Quarter                     $ 24 1/8             $  18 7/8
             Second Quarter                      23 1/4                19 3/4
             Third Quarter                       22 3/8                17 5/8
             Fourth Quarter                      23 1/8                16 5/8
</TABLE>

TRANSFER AGENT AND REGISTRAR:
First Chicago Trust Company of New York
P.O. Box 2500
Jersey City, NJ 07303-2500
201-324-1225
www.fctc.com
fetc@em.fenbd.com

ANNUAL MEETING OF SHAREHOLDERS:
April 24, 1998, 9 a.m.
Cox Corporate Headquarters
1400 Lake Hearn Dr., NE
Atlanta, GA 30319

FORM 10-K:
<PAGE>
 
Cox Communications' Annual Report on Form 10-K as filed with the Securities and
Exchange Commission is available free upon written request to: Finance
Department, Cox Communications, Inc., 1400 Lake Hearn Dr., NE, Atlanta, GA
30319, 404-843-5000, Ext. 6454.

COMPANY INFORMATION:

Communications regarding stock transfers, lost certificates or account changes
should be directed to the transfer agent. First Chicago Trust Company of New
York. For other information, contact one of the following:

Analysts and Institutional Investors: Mark Major, Director of Finance, 404-843-
5447, fax: 404-843-5939

Individual Shareholders and News Media: Anthony Surratt, Director of Corporate
Communications, 404-843-5124, fax: 404-843-5777

INDEPENDENT AUDITORS:
Deloitte & Touche LLP
100 Peachtree St.
Suite 1700
Atlanta, GA 30303-1943
404-220-1500

(c) 1998 Cox Communications, Inc. All rights reserved. Cox, Cox Communications,
the Cox Communications logo, Cox Digital TV, and Cox Digital Telephone are
registered trademarks, trademarks, or service marks of Cox Communications, Inc.

@Home Network and the @ ball are registered trademarks of @Home Network.

Designed by Corporate Reports Inc./Atlanta

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