The single stage residual income model has V0 = B0 + ((ROE - r) x B0) / (r - g)
The residual income valuation model has V0 = B0 + RI1/1+r + RI1/(1+r)^2 + RI3/(1+r)^3… Both of these use RI in the numerator, but why do they have different denominators?
Single Stage model is similar to the Gordon Growth Model in which there is a constant growth rate. When there is a constant growth rate you can discount it by r-g to get the present value of all future cash flows. This is analogous to the FCFF1/WACC-G formula, and the direct capitalization method for Private Real Estate.
The reason why the individual RI numbers are discounted at r is because these are growing at a specific rate which wil be different from the terminal rate growth. In fact for any valuation in which you are individually discounting cash flows, it is because the early cash flows are growing at a different rate than the terminal growth. The terminal value for the second residual income valuation you have there would in fact have a Terminal value at the end where the discount rate would also be r-g. Hope that helps man!
I believe you are referring to the Mendonsa question in the Afterenoon CFA mock right? I got stuck w/ that question too…so, ther will be no growth in this case, only a constant return on the income. The terminology is a bit confusing, by terminal I could understand that it drops to zero also.