From what I've heard it may actually be cheaper than the current CPL/IR as ALL flying training can be done on a single engined a/c.
For the self financed I imagine the cost will be more than a current Integrated scheme. The MPL is hinted as requireing 10 hours SEP and 50-60 hours full motion high fidelity (not sure what the proper term is) sim (737, A320, etc). For this reason, it will be cheaper for the likes of BA to train ab initio as they can further maximise the existing investment in their simulator and training infrastructure.
The course will incorporate a type rating and a mulit-crew IR. The license already exists, it is the syllabus that doesn't. Obviously, you will only be able to apply for jobs with airlines that require your type rating. To fly single pilot or another type would incur further expense.