Here's the graph...

Indeed, that graph doesn't depict what I thought it did, so my apology applies.

But I still can't for the life of me figure out what you're trying to do here.

It is in essence a graph of the price to book value over time. The use of log/log makes sense to get all the points to fit on the graph, but I don't see any way in which it's meaningful to the problem. The growth rate over time has slowed making the data points more clustered where the numbers are bigger in log space, so the fit gives higher weight to recent data points, but that's a small effect.

But all it is really saying is that
* the average price to book ratio has been in a relatively narrow range (or at least seemingly so if you compare it to the 4-5 orders of magnitude of growth over time), and
* that formula fit suggests that P/B has been rising over time. e.g., with book value 50k the fit formula suggests P/B of 1.34, with book value of 100k it suggests 1.46, and with book value of 500k it suggests 1.545.

If you consider the current point on that trend line, feeding in book to get a notion of the "normal" price to expect, you're implicitly assuming that the very long run log trend of P/B will hold, and that P/B will continue to rise. I for one would not place any weight at all on either of those assumptions.

My two concerns here are that (a) it doesn't seem to be a very wise way to come up with the trend of P/B compared with simply looking at P/B figures through time, and (b) it doesn't seem to be true in any useful way. Consider the P/B in the last 30-or-so years. In the first half it averaged 1.726, and in the second half it averaged 1.400. Not much of a long term up-trend.

I think you're better off with KISS. Estimate a reasonable guess of what the "normal" P/B might be now and in the next few years, informed by history. "Informed by" meaning in whatever way seems most appropriate to your observations of the trajectory of the slowly changing structure of the firm. Multiply current book (or peak-to-date book) by that number.

Lately I've been estimating price trajectory by looking at possible future average P/B numbers of 1.37, 1.40, 1.45 and nominal growth rates of 1.5%, 2.0%, and 2.5% per quarter, just to get a cloud of reasonably plausible futures over the next couple of years. As a hobby I've been writing calls whose exit dates/prices are entirely above the cloud, and puts whose entry dates/prices are entirely below the cloud.

Jim