I've been looking over the data for the period Dec '99 to Dec '24, and by my estimate IV/BV has increased quite smoothly from 1.35 to 1.60 over the period, with an r^2 of 0.99. These estimates are based on the weighing machine model, in which the stock price is plotted against BV over a long period of time, and the trendline at any point on the curve is taken as an estimate of IV.

Repurchase prices have been consistent with these estimates. For example, in March 2024 Buffett repurchased A-shares at 1.567x BV, and then on Sept 1, 2024 he issued shares to the Scott family at 1.565x BV as part of his purchase of their BHE shares. The recent $38 billion decline in the value of BHE, as inferred from Buffett's purchase prices of BHE in 2022 and 2044 (with no decline in the BV of BHE) should drop the IV/BV of Berkshire Hathaway shares from someone close to 1.60 to about 1.51 (Buffett's only explanation given for the decline in BHE's value was "Sometimes the value of a company declines.") However, I have to think that the 1.565x BV at which that Buffett issued B-shares to the Scott family is pretty close to his estimate of IV.

For the moment I'll stay with 1.56x BV as my best estimate of IV, while recognizing that no valuation method gives IV to better than about plus or minus 7% or so.