"It looks to me like the abrupt changes in the rate of BV growth in '81 and '99 were a result of the abrupt changes in the rate of growth of the S&P 500 index in '81 and '99."

My guess is that neither the S&P 500 index nor Berkshire's book value per share will grow as fast from Dec 2021 to Dec 2031 as they did from Dec 2011 to Dec 2021, when they grew 12.3%/yr and 12.1%/yr respectively (least squares). I would guess that the S&P 500 index will grow closer to 5%/yr from Dec '21 to Dec '31 (It's already down 19% in 2022, and valuations are still high.), and that Berkshire's BV/share will grow closer to 8%/yr (possibly lower if Warren passes the reins.)

While Berkshire's BV/share growth has been more or less constant since Dec 2000, and since Dec 2011, I'd be cautious extrapolating the same growth rate to the next 10 years. Just mho.