* Forecasts 1st-quarter adj EPS of $0.51 to $0.55 vs est $0.49
* Expects revenue $426 mln to $442 mln vs est $412.8 mln
* Shares rise 18 pct in after-market trade
(Adds forecast, details from conference call, background; updates share movement)
Feb 5 (Reuters) - Akamai Technologies Inc forecast better-than-expected results for the current quarter after the internet content delivery service provider renegotiated pricing terms with its biggest media client.
The company did not name the client but analysts identified the customer as Apple Inc.
Akamai's shares, which rose about 5 percent in post-market trading after the results, jumped as much as 18 percent on news of the renegotiation.
The company warned in October that its fourth-quarter revenue was at risk due to the negotiations.
Akamai on Wednesday forecast first-quarter adjusted earnings of 51 cents to 55 cents per share on revenue of $426 million to $442 million.
Analysts on average were expecting adjusted earnings of 49 cents per share on revenue of $412.8 million, according to Thomson Reuters I/B/E/S.
Akamai has gained from a surge in internet traffic as more people take to social media and its 147,468 servers carry content for clients including Facebook Inc.
Demand from its media and entertainment clients also helped Akamai report fourth-quarter results ahead of analysts' estimates.
Akamai's revenue rose 15 percent to $436 million in the fourth quarter in part due to a jump in online shopping during the holiday season and game title releases.
Net income rose to $80.3 million, or 44 cents per share, from $68.3 million, or 38 cents per share, a year earlier.
"This is one of those really nice quarters where everything went well ...," Chief Executive Tom Leighton told Reuters.
Excluding one-time items, the company earned 55 cents per share.
Analysts on average had expected earnings of 52 cents per share on revenue of $422.4 million.
Akamai shares closed at $47.42 on the Nasdaq on Wednesday.
(Reporting by Chandni Doulatramani in Bangalore; Editing by Don Sebastian and Sriraj Kalluvila)