That mandate is the issue as is the Limited Partners (LP) wishes. Ultimately CX needs to keep their LP's on side for future fund raisings.
I will post a link to a historical, but detailed look at PE strategies and exits in India and China. Main point to take is that a larger portion of exits by PE in India happen as M&A than IPO's. The report also highlights how blue sky and first mover status is more highly rewarded than in China, which makes IPO attractive, where in India this is not so much the case.
You could replace China with other markets in the world that reward blue sky etc. That is why I said managing expectations is very, very important, as meeting them supports the blue sky you are selling and adds value.
In short a script/cash deal through a M&A transaction would not be unusual for an Indian PE exit. You will probably find the shareholders will not be so much CX, but the underlying LP institutions who made up the initial fund for investment by CX.
