Turnaround specialist Melrose Industries has upped its offer for engineer GKN to 467p per share, or £8.1bn, from £7.4bn.
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The deadline for accepting the final offer by Melrose, which would see GKN shareholders own 60% of the company and receive £1.4bn, is Thursday 29 March at 1300 GMT.
GKN said the new offer is still "entirely opportunistic" and "fundamentally" undervalues the group and its prospects.
The sweetened offer comes after GKN announced on Friday that it had agreed to combine its automotive business, Driveline, with US-based Dana in a deal valued at around $6.1bn.
Under the terms of the agreement, which GKN said represents an acceleration of its strategy to separate its aerospace and auto businesses, the company will receive cash proceeds of $1.6bn. GKN's shareholders will also receive 47.3% of the fully diluted share capital of the newly formed company, Dana plc, at completion of the proposed transaction.
Melrose, which said its final offer "will not be increased under any circumstances", said the Dana deal is a "hasty and ill-thought-through transaction" that is prejudicial to GKN's shareholders.
Melrose chairman Christopher Miller said: "On the one hand you can join us on a journey of value creation by investing in a UK listed manufacturing powerhouse worth over £10bn today and receiving £1.4 billion of cash.
"On the other hand your board is attempting a hasty fire-sale of GKN businesses before they have been given a chance to reach their potential and with damaging consequences, we believe, for all stakeholders.
The potential transaction with Dana, if it is allowed to go ahead in the last quarter of this year, would leave you with a minority stake in a foreign listed group run by a Dana management team based in Ohio.
Many of you may not be able to hold the shares being offered by Dana as part of the consideration as they will not be listed in the UK. It is surprising that the GKN board would recommend such a transaction knowing that it is likely to require a forced sale of Dana shares, a fact that will be anticipated by the US markets.
"Private UK shareholders should also be aware that they would be liable to income tax on the value of any new Dana shares they receive. This transaction would involve a lengthy and uncertain completion process, including anti-trust clearances in the EU, US and China, as well as Dana's shareholder approval, which is not expected until the last quarter of 2018." ■