* Says ADHD and rare disease businesses could thrive apart
* Raises full-year earnings forecast after strong first half
* Second-quarter earnings per share rise 11 percent
* Shares give up gains to trade down 2 percent (Adds further quotes, reaction, background)
LONDON, Aug 3 (Reuters) - Shire, the London-listed pharmaceutical firm built up by acquisitions, said it might spin off its hyperactivity drugs business into a separate company and focus solely on rare disease treatments.
Chief Executive Flemming Ornskov said the recent approval of its newest ADHD (attention deficit hyperactivity disorder) drug, and strong demand for its blockbuster Vyvanse, meant the business could thrive as a standalone company.
Analysts said the division, which markets amphetamine drugs to children and increasingly to adults as well, could be worth as much as $8.5 billion.
"The critical strategic decision before us is to determine how best to manage and operate these two businesses in a way that ensures that each has the appropriate level of management focus, investment and strategic flexibility," Ornskov said.
The decision to review the business came as Shire upgraded its full-year earnings forecasts after a strong second quarter.
Ornskov said a split was the natural evolution of the plan he laid out when he joined in 2013 to make the company an undisputed leader in rare diseases.
"I set out a clear strategy of refocusing the company overall on rare diseases, through a series of acquisitions, in particular of course Baxalta," he told reporters on Thursday.
Shire bought haemophilia specialist Baxalta for $32 billion last year in its biggest deal, helping product sales rise 55 percent in the second quarter to $3.59 billion.
That deal dwarfed the $186 million Shire paid 20 years ago for Richwood Pharmaceutical, the owner of amphetamine-based ADHD drugs Dextrostat and Adderall. A decade later it agreed to buy New River Pharmaceuticals, just before Vyvanse was approved.
The drug remains an ADHD market leader and in 2015 it was approved to treat binge eating disorder. It had sales of $518.2 million in the last quarter. Shire's newest ADHD drug, Mydayis, received U.S. approval in June.
"This approval, and its pending launch, further underscores our success in creating a sustainable franchise and our continued commitment to innovation in ADHD," Ornskov said.
Analysts at Berenberg said a spin-off would be welcome news and a back-of-the-envelope calculation based on cash flow suggested a valuation of $8.0 billion-8.5 billion, although it was not yet clear if that level could be achieved.
"It would remove Shire's exposure to the patent cliff for Vyvanse in 2023, a major overhang for the stock, as well as inject cash into the balance sheet to help drive deleveraging," they said.
Liberum analysts said they could see the logic of a listing for the business, which accounts for 17 percent of Shire's revenue, rather than a sale to a big rival because there was little scope for further cost cuts and a question mark still hangs over the use drugs to treat hyperactive children.
Shire, which is based in Ireland but generates most of its sales in the United States, had second-quarter revenue of $3.75 billion and non-GAAP earnings of $3.73 per ADS (American Depositary Share), up 11 percent and above the consensus $3.60.
It also upgraded the midpoint of its full-year earnings per share forecast by 10 cents to $15, reflecting its first-half performance and stronger than expected cost savings from the Baxalta deal.
But Shire nudged down estimates for full-year product sales to $14.3 billion-$14.6 billion, from $14.5 billion-14.8 billion, due to a new generic rival to its gastrointestinal drug Lialda.
Shire's shares retreated from gains after the results were published to trade down 1.9 percent at 4,116 pence by 1506 GMT. (Editing by Susan Fenton and David Clarke)