"littleps" wrote:
Financial lease calculations.

First, given the obvious professional liability of the situation,
it behooves you to continue to seek professional assistance
from a known-competent source. You should not assume
that anyone in cyberspace is competent or is who or what
they say they are. You have obviously already tried that by
talking to a colleague. It might be worthwhile to pay for some
advice from a CPA or similar professional. You can probably
write off the expense of the consultation.

I can tell you that I have no experience with financial leases.

There is an asset of fair value @ 3,512,000. There are
4 payments €“ 150,000 quarterly and yet the last one
(after year) is purchase of this asset @ 3,200,000.
Quaterly payments are made in advance. [....] A colleague
of mine told me that because of advance payments IRR
should be calculated as
IRR(3,362,000€¦150,000€¦150,000€¦150,000€¦3,20 0,000)
saying that initial fair value should be decreased by 150,000.
But as I as I understand it should be like
IRR(3,512,000€¦150,000€¦150,000€¦150,000€¦150, 000€¦3,200,000)

Both answers are correct, depending on details that you fail
to provide. See my questions below.

Your problem seems similar to an example in the HP 12C
Owner's Handbook (p.177, Rev E, c. 1982). You might look
there for more guidance.

In either case, one important fix: the first term should be
negative: -3,512,000 or -3,362,000.

Some other details to take into consideration when formulating
the exact IRR expression:

1. You wrote "4 payments €“ 150,000 quarterly and yet the last
one (after year) is purchase of this asset @ 3,200,000". That
sounds like 3 quarterly payments of $150,000 and a 4th
quarterly(?) payment of $3,200,000.

That is __not__ what your IRR formuation does. Your IRR
formulation has 4 quarterly payments of $150,000 and a
5th (quarterly?) payment of $3,200,000. Your colleague's
formulation has 3 quarterly payments of $150,000 and a
4th quarterly(?) payment of $3,200,000.

2. It is unclear from your English description and from your
IRR "pseudocode" (i.e. not exactly written in Excel form)
whether the quarterly payments are at the end or beginning
of each quarter.

Your formulation suggests that the 1st $150,000 is paid at
the end of the 1st quarter. If, instead, the 1st $150,000 is
paid at the beginning of the lease period, the first cash flow
should be -3,512,000+150,000 = -3,362,000. In fact, that
might what your colleague had in mind.

3. It is unclear from your English description and from your
IRR pseudocode whether the $3,200,000 is paid in the
same period of time as each of the other payments. You
wrote "after year". That sounds like the beginning or end
of the 13th month after beginning of the lease.

If that is the case, use XIRR (for uneven payment periods),
or if you use IRR, be sure to use the same period of time
for each cash flow -- for example, monthly -- using zeros
to fill in periods between quarterly payments.