France Télécom has made an all-stock offer for the shares it does not own in its mobile telecommunication subsidiary Orange, at a premium of around 20% over the market price.
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Chief executive officer Thierry Breton said the move would allow the two companies better integration of their offerings.
"My strategic vision for France Télécom is of a more and more integrated group that knows how to make the most of co-operation between its activities," he said.
Since France Télécom sold part of Orange to independent shareholders in 2001, the companies' situations have changed in a number of ways.
The mobile telecommunications industry has matured, and France Télécom and Orange now have similar financial characteristics, making them a better fit, Breton said.
One of the motives for floating Orange was to allow it to acquire other companies in all-stock transactions, something that is impossible for France Télécom, as a significant acquisition would dilute the French government's holding below the 50% required by law.
However, the French government indicated in July that it will soon remove the rule requiring that the state hold a majority of the company.
France Télécom offered to exchange 11 of its shares for each block of 25 Orange shares. On Sunday, the friendly offer received the unanimous support of Orange's board, according to a joint statement from the two companies.
The offer will be open from 12 September to 7 October. If at the end of that period France Télécom holds more than 95% of Orange's shares, it may move to buy back any outstanding shares. France Télécom holds 86.28% of the shares at present.
The move only concerns Orange, Breton said, and not France Télécom's internet service provider subsidiary Wanadoo.
Wanadoo's ratio of price to earnings is still around four times that of France Télécom; there is not the same financial similarity as with Orange, Breton said.
Peter Sayer writes for IDG News Service