Well, for an stake to be worth $100 per share in gains potential, the gain has to be about $2.2bn. Both companies would need to IPO at $10bn or higher to produce such a gain, and that's before tax. Maths below - mostly from memory so apologies if I have made a stupid mistake.
Fairfax owns 20% of Ki. Even assuming it is carried at zero, to generate a $2.2bn gain it needs to IPO at a valuation over $10bn. That's over 10x GWP on the platform and strikes me as an optimistic number unless we have a very strong thesis that Ki has a deep competitive moat.
FFH owns 29% of BIAL (42% of FIH which owns 69% of BIAL after the recent addition). FIH carried 59% of BIAL at $1.6bn in q3 and the recent 10% addition cost $255m, so the threshold for gains on FIH's 69% is $1.85bn. That implies $2.7bn for all of BIAL and $770m for FFH's 29% (excluding any impact on performance fees). To produce a $2.2bn gain to FFH BIAL has to IPO at $770m + $2.2bn = $3bn for 29%, or just over $10bn overall, or 4x the valuation that Siemens have just realised.
As I said - seems high to me. But if you have evidence that I am wrong, I'll be delighted.