* Rejects 405 p/shr offer from Melrose
* Appoints Anne Stevens as CEO
* To separate business into two divisions
* Shares up 20 percent after October warning (Adds background, shares)
LONDON, Jan 12 (Reuters) - GKN has rejected as "entirely opportunistic" a takeover offer from turnaround specialist Melrose and set out plans to split its business to boost profitability, sending shares in the British engineering firm up 25 percent.
The maker of components used in the Black Hawk helicopter and by automakers such as Volkswagen and Ford cut its profit outlook in October, hurt by a writedown at its U.S. aerospace division.
It later warned the writedown would be bigger than expected and announced the departure of CEO-designate Kevin Cummings, the head of the aerospace division who had been set to take over the top job this month.
On Friday, the 259-year-old group named former Ford executive Anne Stevens as CEO, a role she has held on an interim basis since November.
It also set out her plans to separate GKN's aerospace and automotive divisions to improve profitability.
The Melrose offer valued GKN at 405 pence ($5.48) per share. GKN's shares jumped by 27 percent to 423 pence in early Friday trading while Melrose was up 11 percent. A source familiar with the matter said Melrose planned to continue to pursue its bid.
The board of GKN said it had considered the proposal. "(We) unanimously rejected it, having concluded that the proposal is entirely opportunistic and that the terms fundamentally undervalue the company and its prospects," it said.
A downturn in GKN's performance had reignited speculation it might separate its two divisions and restructure the business, which employs 58,000 people across 30 countries.
GKN said on Friday it had launched a wide-ranging review in 2017 to identify why its profit margins and cash generation were coming in below expectations, despite growing sales.
On Friday it said it would instill a stronger performance and accountability culture after the October profit warning which stemmed from a failure to improve productivity at its U.S. Alabama plant.
The site produces composite structures and complex machine parts for aircraft such as the Black Hawk helicopter.
GKN will separate its aerospace and engineering businesses, giving them distinct investment profiles and capital allocation policies. While that plan does not yet entail a full separate listing, it could make one possible in the future.
"The board will communicate further details on the optimal method of separation in due course," it said.
Melrose, valued at 4.16 billion pounds at the close on Thursday, specialises in buying companies that it can improve through investment and cost cuts with the aim of selling them at a profit.
GKN was valued at 5.7 billion pounds at the close of Thursday.
($1 = 0.7385 pounds) (Reporting by Kate Holton; additional reporting by Ben Martin; editing by Costas Pitas and Jason Neely)