In your example, they had $100 of book in year one. If they are like a current median big firm, they are earning 16.7%, so $16.70 net profit.
In year two they had $107 of assets in year two. Since typical ROE is high, that was a bad year, but let's go with it.
But year two is typical for returns and they earn the currently typical l6.7% on assets, or $17.87 on $107 in assets.
The difference is $1.17/year. Would you pay more than $7 for earnings of $1.17? I would.
If so, then the $7 in retained book is a worth a multiple considerably greater than 1.

If the company earns more than 7% on its reinvested earnings, it would grow its BV more than 7%. So in your example, BV would grow by $8.17 to $115.17 in year 2, which is 7.6% growth in BV. That would be in our example outperforming the market.

I guess a simpler way of saying this is BV would grow at the rate of ROE in absence of dividends and buybacks. So if you assume BV would grow at the same rate as the market, it should not be worth more than the book value. Any premium to BV must be due to expectations of outperformance over the market.

So if you expect BV to grow at 8% over long term and expect market to return 8% over long term, does it still make sense to value BRK at a BV multiple higher than 1x?

Thanks for indulging me on this. I valued BRK half a dozen ways and they cluster around 1.5x BV. But when I assume that it would provide returns equal to market, I keep thinking it should not be valued at 1x BV. I cannot quite square these two.