Re: Discount Rate Question

On Sep 9, 10:19 am, Axel Vogt <&nore...@xxxxxxxxxxx> wrote:
Ray Vickson wrote:
On Sep 8, 1:18 pm, Axel Vogt <&nore...@xxxxxxxxxxx> wrote:
Rob Bain wrote:
Hi
If I have the NPV of a cash stream calculated with a discount rate of
8%, and the NPV of the same cash stream calculated using 6%, can I
calculate the NPV at 3.5%?
I don't think this is possible (no unique solution) - but I'd be very
interested in members' views. Is there, for example, an 'approximate'
or 'most likely' solution???
Thanks,
Rob
30 years ... only two "inputs" ... here is a brute way:

If I understand correctly you want to know the interal rate
of return having two different inputs, time is 30 years, yes?

Here is a brute way:

Determine r1, such that exp(-r1 * t ) = your first NPV and r2
your 2nd NPV (same formula, t = 30) using the log function.

This won't work. NPV1 = sum(X_n*exp(-r1*n),n=0..29) is not of the form
exp(-r1*T) for any T. Basically, the OP has NPV1 as above and NPV2 =
sum(x_n*exp(-r2*n),n=0..29) (or, instead of exp, maybe 1/(1+r1)^n,
etc.) He has two equations in the 30 variables x_0,...,x_29, so there
will be infinitely many possible solutions. I don't think the OP can
have what he wants, and even approximations seem unavailable. For
example, one could try to represent the "exp" exp(-r*n) as a simple
linear combination of exp(-r1*n) and exp(-r2*n) (although, due to
convexity, that would be an /overestimate/), but even that would
require knowing sums of the form sum(n*x_n*exp(-r1*n)) and
sum(n*x_n*exp(-r2*n)), which have not been given.

I think the simple answer is NO.

The point is: the present values are the same for the paths.

It works, it is getting rates from discount factors. May be I was
not clear enough, so: NPV1 = sum(X_n*exp(-R1*n),n=0..29) is given,
R1 his 8%, so NPV1 * finalValue = exp(-r1*t) * finalValue can be
solved for r1 (t is a fixed value, not a variable) and then the
r3 is guessed through linear interpolation ignoring convexity
(cf Jannick's reply).

So how do you explain the fact that it's possible to construct two
sets of cashflows such that in both cases the NPVs at 8% and 6% match
given values, and yet the NPVs at 3.5% are totally different?

.

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