word usage - Is it possible to use 'shall' for intentions? is PEU wrong here?

M.swan PEU (3rd edition-unit:217) says,

" Topic: announcing decisions: will

We often use will when we tell people about a decision as we make it.for instant if we're agreeing to do something.
               e.g:1. OK. we'll buy the tickets.
                      2.The phone's ringing. I'll answer it.

Shall is not used in this way.
               e.g:You can have it for $50. -OK.I'll buy it. (NOT: I shall buy it) "

According to this, we can't use shall (with first persons) for intentions or decisions which made at the time of speaking.but the book 'Cambridge Grammar Of English' and these web seits( 1 , 2 ) say that shall can be used to announce intentions or decisions. for example,

• I don't want anyone with me.I shall do this on my own. (reference:CGE)


• I shall contact you again when I have further information.

So my questions is, is it possible to use shall for intentions or decisions as we make them(with I&we)? [if the answer is Yes ,Why do PEU say "shall is not used for decisions "]

I searched on the internet and read lot of grammar book but I could not find a clear answer to this confusion.so any answer is appreciated.