Residual Income EOC question pg. 625

I understand taking the present value of the t1-t5 RIs, but the solution states that the way the terminal value has been calculated is taking 20% of 20.11 (which is the t5 ending BV). This has thrown me off. The items set states that there will be a 20% premium to bookvalue at the end of five years. So its hard for me to understand why this would not be (1.20*20.11). any guidance would be much appreciated Thanks, Andrew

nevermind on the above, I got it now. It’s only the premium that is discounted along with RI’s for t1-t5 and added to the beginning book value.

Bo-ROE(BO)/r-g

actually nyc this will result in exactly the problem I described in the original post. The solution is actually that you only want to include the premium along with the final residual income amount and discount this back to the present. Otherwise you double count the book value which has already been added at time 0 (or the beginning of the RI valuation equation)