It’s taken me some time, but I still don’t get it.
Why is justified p/b ratio = (ROE - g)/(r-g)
I wrote an article on justified ratios that covers this, including its derivation: http://financialexamhelp123.com/justified-ratios-price-multiples/
It might help to think in terms of stabilized cash flow to equity: net income = BxROE = cash flow to equity; net reinvestment = Bxg (since book value will grow at the rate of g). hence stabilized net cash flow to equity = (BxROE - Bg). This cash flow is growing at g%, cost of equity = r%.
Using DCF formula for growing cash flow: P = (BxROE - Bg)/(r-g)
Rearrange to get the P/B formula