Brain teaser

fucking infinity

pv of infinite cash flows:

pv= Σcf/(1+r)^t = Σ(100*t)/(1+0.05)^t

PV= 100/(0.05)*(1/ 1-(1+0.05)^-t))

let's say t=20y:

=100/ (0.05)*(1/(1-0.677429))

=100/(0.05)*(1/0.322571)

=6160

i think this is right, someone correct me if i'm wrong

Deleted

Yeah I think this is infinity because the way the cashflows work ($100 more per year as time passes, i.e. $100, $200, $300…), it’s like a stack of perpetuities. You can value a single perpetuity by discounting but can’t discount an infinite sum of them.

I don’t think it will be infinity as the increase in t will make the discounted cashflow 0 beyond a certain point (e.g. 100,000 dollars discounted to the power of 1,000 will be close to 0 if the discount rate is above 1%) 

However, without knowing the discount rate it will be impossible to know the exact value (and even then you would need a computer to find it) 

So you are essentially receiving a $100 dividend each year. I would use Gordon growth method where

Intrinsic Value = Terminal CF * (1 + perpetual growth rate) / ( discount rate - perpetual growth rate)

The growth rate would be 0% since dividend stays $100/ year. I’ll use discount rate of 8% cause stock market.

V = $100 * (1 + 0%) / (8% - 0%)

V = $100 / 8% = $1250

(@ 5% = $2000 , @ 3% = 3,333)

In other words $100 into perpetuity is the same as receiving $1250 today iff your alternative investment returns 8%.