I’m having trouble conceptually understanding the PV of a terminal value, specifically how many years we should be discounting the CF. For example, for residual income using a persistence factor, the final year residual income is discounted by 1 + required ROE − persistence factor, and then discounted again by (1+r)^t-1. When residual income is expected to continue persistently, the last year residual income is discounted just by r, and then by (1+r)^t-1. On the other hand, if the final cash flow of residual income is calculated using a premium over book value, it is discounted on a t basis (in year 5 the premium would be discounted by (1+r)^5). In my first two scenarios, why wouldn’t the terminal value be also be discounted on a t basis instead of t-1? Sorry if this is poorly worded but its becoming quite frustrating that I can’t wrap my head around this.
_ In this example the premium over book value is for year 5 so in order to arrive at present value we discount by 5 years _
Assuming there are 5 periods and we are in 2010, and the question states something like after 5 years i.e in 2016 the ROE will start to decay towards required return with a 60% persistence factor. As per usual the Terminal Value should be at T5 because that is the period where our final cash flow is. To my understanding you discount the terminal value which is computed as (RI5 x 1+g) by (1+r-w)^t-1 so that the discount of the terminal value is in line with the last cash flow at t5. If you did t it would be discounted by 6. I just checked the curriculum questions number 24 under residual income has a relevant question which uses the above logic. Hope this helps.
Example : To determine terminal value (at the end of Year 4) we also need to calculate the dividend payment for the first year of the constant growth period (Year 5):
D(5) = D(4) * (1 +g)
We then calculate the terminal value (at the end of year 4).
V(4) = D(5)/ (r-g)