Robert Hagstrom calculated intrinsic value in his book The Warren Buffett Way, but he didn't derive any mathematical proofs. This was probably to keep it relatively simple. The equations would show what would happen to the investment under 3 different conditions:
1) bond grows faster than the company 2) bond grows slower than the company 3) bond grows at the same rate as the company
Hagstrom only had examples of when #2 was true.
After being confronted by an individual who wanted the proof (I wasn't able to produce it at that instant), I went back to my desk and scribbled it out on a scrap piece of paper at work (I couldn't concentrate after that kind of challenge).
Basically it just shows mathematically what is intuitive. That is, that if a company grows slower than a bond, buying the bond is more prudent etc.
For anybody who wants to try it, just derive the Future Value forumula (using P=present value, F=future value, I=interest rate, n=time in years). This formula applies both for the bond and the company. This is supposedly Buffett's first method of finding the future worth of a company.
Then equate both future values F(bond) = F(company). This is equivallent to 'discounting'.
When you get to the bottom of the solution you will have three solutions. I(bond) > I(company), I(bond)=I(company) and I(bond) < I(company).