My property is being reassessed for property tax purposes.  For each 
$9000 in increased valuation, property taxes are increased by $100.00
a year.  Each year assessments are increased by 2%.  Assuming I
continue to own the property for 15 years,  what amount could I
presently pay for professional help in appealing the increased
assessment that would make financial sense.

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Request for Question Clarification by pafalafa-ga on 26 Feb 2003 17:42 PST

There might be researchers out there more clever than I am (actually,
I'm *sure* there are!), but it seems to me this question can't be
answered without knowing the current value of the house.

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Request for Question Clarification by pafalafa-ga on 26 Feb 2003 17:43 PST

Make that the current *assessed* value (not the market value, which is
often very different).

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Clarification of Question by orte-ga on 27 Feb 2003 08:40 PST

The question does not relate to property values. It relates to upkeep
costs.  It would clarify to assume the cost of money, let's say at 5%

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Request for Question Clarification by nauster-ga on 27 Feb 2003 10:13 PST

There is no way of answering this question without knowing what the
difference between the present assessed value and the probable
re-assessed value is.

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Clarification of Question by orte-ga on 28 Feb 2003 20:59 PST

Knowing assessed value is not necessary.  The question relates only to
the present cost involved (ie appealing the assessment - a variable)
against the future known costs ie. an increase in taxes over 15 years
of $100 a year per $9000 in assessments.   In other words what is the
present value(cost)of the amount of taxes that must be paid over 15
years, including increases of 2% per year.  The cost of capital being
figured at the rate of 5%

orte,
The clarifications to your question have been most helpful. I now feel
I understand your question well enough that I can answer it.

---The short version of the answer---
Each $100 increase is going to cost you $1175 over the next 15 years,
present value.

---How the number was arrived at---
The standard present value calculation assumes that the stream of
payments are all of equal amounts. Since your stream increases by 2%
per period, the standard formula cannot be used. Fortunately, there is
Excel.
I set down the series of 15 payments: $100, $102, $104.04, etc, each
2% bigger than the last. Then, for each payment, I deflated its value
based on how many years in the future it is, assuming a 5% cost of
capital. Then I added all these numbers up to figure the present value
of that stream.
For example, the last payment will be for $131.95, but because of the
5% per year deflator, its present value is only $63.47.
In any event, the sum of those 15 deflator-adjusted payments is $1175.

---Additional Considerations---
At face value, the result of the calculation tells you that you should
be willing to pay up to $1175 per $9000 in extra assessment you
anticipate. HOWEVER:
1) Property tax payments are, under certain circumstances, deductible
when figuring income tax. This means that your real cost might not be
the full $1175, if you recapture some of that in a lower income tax
burden.
2) Paying for professional help is probably not going to give you a
100% chance of avoiding the increased assessment. If you think you
have a 50% chance of winning out, then you should be willing to pay up
to 50% of the potential savings.
3) The number is very sensitive to the length of time, and, to a
lesser extent, your estimate of cost of capital. For example, if your
cost of capital is 2% and the term is 20 years, that's $1961 per $100.
On the other hand, if the cost of capital is 7% and the term is 10
years, it's only $761 per $100. So any number given is going to a
rough estimate only, because you can't be sure about the underlying
assumptions.
4) The number also changes depending upon whether each payment is made
at the beginning or at the end of the year. In other words, is the
first payment now or at the end of the year? My above figure assumes
you pay at the end of the year. If the payments come at the beginning,
the cost increases to $1234 per $100.

Hope that helped, and please don't be bashful about asking for
clarification on any aspect of my answer.

Cheers,
nauster-ga

This was a really good answer and helped me in focus on  the range
betweem possible outcomes, and to judge them in terms of present
costs. Appreciate it very much.

No, it's not necessary to have the current assessed value of the
property to answer your question.

You wish to avoid paying a stream of incremental payments in the
future. Though you may think that stream would last for no more than
15 years, it would actually last forever if successive buyers of your
property inherit your assessment. (When you sell, your buyer will
include future property taxes in her assessment of the property's
value, so it is as if you pay that stream forever.) If, however, the
property is reassessed upon its transfer, then yes, the increase lasts
only that 15 years.

What is that stream? For each $9000 in increased valuation, it is
$100.00 in the first year, $102.00 in the second, $104.04 in the
third, and so on. That stream of future payments has a present value.
In order to calculate that present value, you will need your cost of
capital. With that value, it's a snap to calculate the present value
of the stream.

You should be willing to pay any amount that is less than that present
value to avoid the increased valuation, assuming that you are 100%
certain that your professional help will be successful.

If you're less than 100% certain, you'll be willing to pay less. The
degree of reduction in the sum you are willing to pay depends both
upon your uncertainty and upon your aversion to risk. You can see that
as follows: Suppose I force you to play a game with me. I ask you to
take a coin out of your pocket and toss it. If it comes up heads, I
will pay you $1000, but if tails, you must pay me $1000. You can see
this is a perfectly fair game, even though you are only 50% certain
that you'll win, yet if you're typical, you'd rather not play this
game because losing $1000 would be more painful to you than winning
$1000 would be pleasant. You'd rather pay me a small sum to get out of
playing the game at all. The larger the amount that you're willing to
pay me to get out of the game, the greater your aversion to risk.

You have exactly what I was looking for.  I don't know how to
calculate present value.  That is my question.  I guess I could assume
the cost of capital at 5%. I know there are a lot of variables, but
still have to make a decision based on what is presently known.