The formula for Present value (PV) of PERPETUAL annuity is
PV = Annual Cash flow / Discount rate
I want to know how above formula is derived.
I know that
PV = Annual cash flow / (1+r) + Annual cash flow / (1+r)^2 … and so on till eternity.
But how the value of above formula leads to just
Annual cash flow / Discount rate
P = \frac{CF}{1 + r} + \frac{CF}{\left(1 + r\right)^2} + \frac{CF}{\left(1 + r\right)^3} + \cdots
\left(1 + r\right)P = CF + \frac{CF}{1 + r} + \frac{CF}{\left(1 + r\right)^2} + \frac{CF}{\left(1 + r\right)^3} + \cdots
Subtracting the first one from the second one:
\left(1 + r\right)P - P = CF
\left(1 + r - 1\right)P = CF
rP = CF
P = \frac{CF}{r}
Voilà!
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