How to calculate NPV of an infinite series?
 

I have a series of cashflows, forecast to grow at say 2% each year and
go on indefinitely. Is there a formula or function I can use to get
the value of the maximum net present value of this series? The only way
I can find so far is to model it for 100's of periods, use the NPV
function for each year in turn, then see at what year the NPV stops
changing... must be a better way surely?

Say D is your discount rate, CF the annual constant cash flow. (note that D
must be above 2% to estimate an "infinite" NPV)
NPV = Sum CF* ((1+2%)/(1+D))^N

When N is infinite, after simplification,
NPV = CF * 1 / (1 - r)
where r = (1+2%)/(1+D)

--
A+

V.


"Mike" wrote:

I have a series of cashflows, forecast to grow at say 2% each year and
go on indefinitely. Is there a formula or function I can use to get
the value of the maximum net present value of this series? The only way
I can find so far is to model it for 100's of periods, use the NPV
function for each year in turn, then see at what year the NPV stops
changing... must be a better way surely?

Suppose you start with a value of "s" that grows by a factor of g, and r is
discount rate.

then NPV as the time period tends toward infinity is:
NPV = (g*s) / (r-g)

For your example, g=1.02, and r=1.08

HTH
--
Dana DeLouis
Win XP & Office 2003


"Mike" wrote in message
ups.com...
I have a series of cashflows, forecast to grow at say 2% each year and
go on indefinitely. Is there a formula or function I can use to get
the value of the maximum net present value of this series? The only way
I can find so far is to model it for 100's of periods, use the NPV
function for each year in turn, then see at what year the NPV stops
changing... must be a better way surely?