as for Notes, Equity page 239, i have a question on part 3, here is the quote “Residual income begins to decline after Year 5, so the terminal value in Year 4 includes the present value of Year 5 residual income.” (Tolia 239) can someone help me understand, why is the notes calculate the terminal value at period 4, when the declining phase starts at the end of period 5, shouldnt we be calculating terminal value of period 5 instead? and we should use the last phase, phase 5’s RI, times persistence factor divide by r-g? why not work it like this but use period 4 terminal value instead?
It’s the same as Gordon growth:
P_n_ = D(n+1) / (r − g)
exactly bro… terminal value uses GGM at the perpetual terminal stage.
but here n is the period when the second phase or earlier phase ends, the next phase starts at n+1, in the example, the next phase starts at 6 but the counting ended at period 4, did I miss something? didnt it say the next phase starts when phase 5 ends?
What “notes” are you referring to? Schweser? Without having them and based on what you’re describing, all I can assume is the wording is written poorly or there is a typo. It probably should have said “… begins to decline IN Year 5”.
I don’t know the specific example, but suppose that we have the following residual income values:
- Year 1: $10
- Year 2: $15
- Year 3: $22
- Year 4: $25
- Year 5: $30
After year 5, the residual income for each year will be 80% of the residual income for the previous year. In particular, year 6 residual income is $24.
Suppose that the required rate of return is 10%.
Then:
- Year 1 PV = $9.09
- Year 2 PV = $12.40
- Year 3 PV = $16.53
- Year 4 PV = $17.08
- Year 5 PV = $18.63
We can calculate the PV of all residual income as:
$9.09 + $12.40 + 16.53 + 17.08 + $18.63 + $24 / [(1.1 – 0.8)1.1^5)]
= $9.09 + $12.40 + 16.53 + 17.08 + $18.63 + $49.67 = $123.39
or as:
$9.09 + $12.40 + 16.53 + 17.08 + $30 / [(1.1 – 0.8)1.1^4)]
= $9.09 + $12.40 + 16.53 + 17.08 + $68.30 = $123.39