Hey guys, for the LIFE of me I just can’t seem to understand the formula for the RI Multistage Model with respect to the persistence factor.
V0=B0 +T−1∑t=1(Et−rBt−1)(1+r)t + Et−rBT−1/1+r−ω)(1+r)T−1
When the persistence factor is 1, it means that RI will continue at the same level indefinitely. Substituting 1 Into the equation,
V0=B0 +T−1∑t=1(Et−rBt−1)(1+r)t + Et−rBT−1/1+r−ω)(1+r)T−1
= … Et−rBT−1 / (+r)(1+r)T−1
How does this above change into this below? (How does the bolded denominator just fall off)?
V = B0 + RIt/r
Am I mixing up the perpetuity with the persistence factor?
I think using Schweser and the curriculum’s formulas are confusing me.
Can someone also explain this formula from Schweser?
(PT-BT)+RIT/1+r
I cannot find the equivalent in the curriculum.
Thanks in advance!
You can basically just work with the simple formula to value a “growing” perpetuity. The value V of your growing perpetuity of residual income is:
V(0) = RI(1) / (r - g)
where V(0) is the value at t=0, RI(1) the residual income at t = 1, r the required rate of return and g the growth rate. If you encounter a question with a persistence factor, then all this really does is specify your growth rate g. For example: Say you you are given some value for RI(1) and a persistence factor w = 0.3. What that means is that after 1 year only 0.3 of RI will persist. This is equivalent to g = w - 1 = -0.7. Now just plug in g = -0.7 in the above equation and find the value of the residual income stream to be:
V(0) = RI(1) / (r + 0.7)
If you are given a persistence factor of 1.3 then you are really in the case of a growing perpetuity (g = 0.3) rather than that of a declining stream of residual income. The formulas are all the same though.
Also for w=1 you find g = 0 and V(0) = RI(1) / r. Please note that this is only the value of the residual income stream. To find the value of the corresponding security you have to add the book value at t=0.
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