morebeans

I believe this will do what you're talking about.

Contrib NAV
1/1/2011 -10 10
1/1/2012 0 15
6/30/2012 -1 17.5
1/1/2013 0 21.875

I just made up some data.
I created another column (D) that was NAVt-NAVt-1 for t>1.
And then a column (E) that was Contrib plus the new one.
All you then need is XIRR((E$2:Et,A$2:At) for every t>1 in column F.
If you want you can add one to F to reflect that you get your principal back.