E-commerce investor Prosus NV on Dec. 9 increased its bid for Just Eat PLC to about £5.1 billion in cash, upping the ante in the battle with Takeaway.com NV for control of the U.K. online food-delivery company.

Prosus, a subsidiary of South African technology investor Naspers Ltd., raised its offer for Just Eat to 740 pence per share from 710 pence, or about £4.9 billion, and reduced its condition for acceptance to 50% plus 1share from 75%.

For Just Eat shareholders, the offer from Prosus represents a cash alternative to a share-based acquisition by Dutch peer Takeaway.com. The transaction, unveiled in July, originally was characterized as a merger and was backed by the boards of both companies, but the structure was changed to an acquisition after Prosus tried to break up the deal and to bag Just Eat for itself.

The boards of Just Eat and Takeaway.com have rejected the approach by Prosus and continue to support their proposed combination, which they have said would create one of the world's largest online food-delivery services. The share-based structure would allow Just Eat's shareholders "to share in the significant future value creation potential" of the deal, they said.

However, Prosus has argued that Just Eat requires substantial investment for delivery, product, technology and marketing that would not be available immediately in a tie-up with Takeaway.com.

"Unlike the Takeaway.com offer, which relies on shares remaining at an above-sector multiple, our cash offer provides certainty of value to Just Eat shareholders," Prosus CEO Bob van Dijk said in the Dec. 9 statement. "We urge shareholders to accept our offer, as it is the only one that delivers certainty in the face of undeniable industry change."

Takeaway.com said it recognized the challenges facing Just Eat and planned to use its expertise to overcome them. For example, in London, the largest market for online food delivery in the U.K., it would lower delivery fees to lure more customers and roll out its Scoober delivery service.

Jitse Groen, founder and CEO of Takeaway.com, in a letter to Just Eat shareholders on Dec. 9, described the Prosus bid as a "hostile, low-ball" offer. "If it succeeds, it will keep Just Eat's value-creation potential for itself," Groen added.

Investors appear unconvinced the Dec. 9 offer from Prosus will be the final twist in this saga. Just Eat's shares have traded above 740 pence per share since Nov. 14. In late-afternoon trading Dec. 9, they were up 3.8 pence, or 0.5%, at 780.8 pence.