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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