PPP's always cost more; if the government would just spend from their own balance sheet. The private portion of the costs include the profit that needs to be generated.

The only time a PPP would cost less than a purely public project, is when the people running the public project are so incompetent that they constantly fuck up.

But if the government hired the same people, on the same money as the private sector, they would achieve the same result at a lower cost!
If the government only hired great project managers; and they got the subcontractors to do the relevant bits (like private firms do) they would spend less than a PPP.

PPP's could be a good idea, if you as a government absolutely cannot hire good people.
Some councils are in this position, they simply cannot offer the same rates as the private sector, thus cannot hire the best project managers.