The b P (calc-fin-pv)
[pv] command computes the present value of an
investment. Like fv, it takes three arguments:
pv(rate,
n, payment). It
computes the present value of a series of regular payments.
Suppose you have the chance to make an investment that will pay
$2000 per year over the next four years; as you receive these
payments you can put them in the bank at 9% interest. You want to
know whether it is better to make the investment, or to keep the
money in the bank where it earns 9% interest right from the
start. The calculation pv(9%, 4, 2000) gives the
result 6479.44. If your initial investment must be less than
this, say, $6000, then the investment is worthwhile. But if you
had to put up $7000, then it would be better just to leave it in
the bank.
Here is the interpretation of the result of pv:
You are trying to compare the return from the investment you are
considering, which is fv(9%, 4, 2000) = 9146.26,
with the return from leaving the money in the bank, which is
fvl(9%, 4, x) where
x is the amount of money you would have to put up in
advance. The pv function finds the break-even point,
‘x = 6479.44’,
at which fvl(9%, 4, 6479.44) is also equal to
9146.26. This is the largest amount you should be willing to
invest.
The I b P
[pvb] command solves the same problem, but with
payments occurring at the beginning of each interval. It has the
same relationship to fvb as pv has to
fv. For example pvb(9%, 4, 2000) =
7062.59, a larger number than pv produced
because we get to start earning interest on the return from our
investment sooner.
The H b P
[pvl] command computes the present value of an
investment that will pay off in one lump sum at the end of the
period. For example, if we get our $8000 all at the end of the
four years, pvl(9%, 4, 8000) = 5667.40. This is much
less than pv reported, because we don't earn any
interest on the return from this investment. Note that
pvl and fvl are simple inverses:
fvl(9%, 4, 5667.40) = 8000.
You can give an optional fourth lump-sum argument to
pv and pvb; this is handled in exactly
the same way as the fourth argument for fv and
fvb.
The b N
(calc-fin-npv) [npv] command computes
the net present value of a series of irregular investments. The
first argument is the interest rate. The second argument is a
vector which represents the expected return from the investment
at the end of each interval. For example, if the rate represents
a yearly interest rate, then the vector elements are the return
from the first year, second year, and so on.
Thus, npv(9%, [2000,2000,2000,2000]) = pv(9%, 4, 2000) =
6479.44. Obviously this function is more interesting when
the payments are not all the same!
The npv function can actually have two or more
arguments. Multiple arguments are interpreted in the same way as
for the vector statistical functions like vsum. See
Single-Variable Statistics. Basically, if there are several
payment arguments, each either a vector or a plain number, all
these values are collected left-to-right into the complete list
of payments. A numeric prefix argument on the b N
command says how many payment values or vectors to take from the
stack.
The I b N
[npvb] command computes the net present value where
payments occur at the beginning of each interval rather than at
the end.