Residual income- persistence factor

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afranks1

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Looking at Schweser reading 36 pg 208 for this. The question (only selected parts) says:
Calculate the intrinsic value of the company using a residual income model, assuming that after 5 years residual income remains constant. The answer says the following:
The $0.44 perpetuity beginning in Year 5 is worth $4.40 ($0.44/0.1) in Year 4. The intrinsic value is V0 = 5 + [$0.25/1.1 + $0.29/1.1^2 + $0.33/1.10^3 + $0.38 + $4.40 / 1.10^4] = $8.98
My question is: why are they using terminal value year 4? Question says after year 5 residual is constant, so why are we not using terminal value year 5 = Residual income yr 6 / 1+r -1
 
RI/ (1+r-w). w=1 in this case (constant RI from year 5).
 
Can someone please help on this.
For the next part of the question, they say “after year 5, residual income will decay over time to zero with a persistence factor of 0.4. Calculate residual income.
Answer says: residual income begins to decline after year 5, so the present value in year 4 includes the present value of year 5 residual income. Terminal value in year 4 = 0.44 / 1+0.1-0.4.
Isn’t this saying that year 6 (after year 5) is the first year of decay, so you must use terminal value 5 = RI6 / 1+0.1-0.4. Would really appreciate help on this.
 
Thanks Raw. This is from Schweser Reading 36, haven’t got a cfai example.
More thinking about it conceptually, if residual income declines after year 5, don’t we use terminal value year 5 = Residual income 6 / 1+r-g. As in the first year of decline is year 6, hence we use terminal value year 5?
 
because they said on year 5 it’s constant already. if you think DDM models they always says “after” 4 years volatile growth will be constant growth of 3%. when we see that we always find terminal value at year 4 the last year of volatile growth.
if you think about this question the last year of volatile growth before it’s constant is year 4. that’s why terminal value is year 4
*edit: if im looking at the same question. it says assume instead of after 5 year, it is constant. it’s saying before it was after 5 years NOW it’s constant on 5th year.
 
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