Payments specialist Worldpay Group Plc just got a whole lot more expensive for potential acquirers. Justifying the outlay will probably require patience and long-term reinvention, rather than the quick and easy cost savings some investors prefer.

Shares of Worldpay jumped as much as 29 percent Tuesday after the company said it had been approached by U.S. rival Vantiv Inc. and JPMorgan Chase & Co. about a potential takeover. The expected bid premium looks clean indeed, close to the industry’s traditional 30 percent.

While there isn’t any certainty of an offer, Worldpay is now seen as in play and carries a high price: It trades at 30 times forward earnings and its enterprise value is 16 times forward earnings before interest, tax, depreciation and amortization, more than Vantiv and Denmark’s Nets A/S.

What would justify the excitement?

The payments sector is growing, for one thing, and is ripe for consolidation. Once little more than processing utilities owned by banks, players are now capable of capturing spending growth online and via smartphones. Mobile payments are expected to expand at double-digit rates through 2020, according to CapGemini. Buying this growth through acquisitions is already happening, and the recent arrival…