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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.
Answer should be 250,000 (@ 2% discount rate)
If you think about it as each tree starting in Y1, Y2, … , Yn producing a fixed stream of $100 each year when it starts, then you have a $100 perpetuity starting from Y1 onwards
Then, each year’s respective PV is $100 / (r-g) = $5,000 at r = 2% (remember each individual tree isn’t growing cash flows, rather there is just 1 additional tree starting each year)
Now what you have instead is a stream of $5,000 cash flows each year from Y1, Y2, … , Yn which can again be discounted at the growing perpetuity formula to get $250,000 at 2%
Sorry if bad formatting, on mobile
This is very close. I'm too stupid to figure out why the following is the case quickly, but the answer is actually 255K at 2%. So what you said plus the original PV of 5k.
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%.
If I understood the question correctly, I don’t think the dividend stays the same. I believe it is modeled such as the dividend for year n is equal to n*100
As such, terminal growth cannot be easily determined as a % ( 300 is 50% more than 200, but 400 is 33% more than 300)
you might be right, but I've been asked a variation of this question where it was assumed constant $100/year into perpetuity (what value would I put on such a tree).
Otherwise the above answer is right. Each tree at 8% discount rate producing $100/year is worth $1250. Now you have 1 new tree/year…so you are just simply repeating the formula. Essentially you’re valuing infinite amount of trees with each tree’s value $1250 (same as single tree problem).
$1250/8% = $15,625.
(@2% discount it’ll be $250,000.)
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