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Q: financial calculation ( Answered ,   2 Comments )
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 Subject: financial calculation Category: Business and Money > Consulting Asked by: orte-ga List Price: \$35.00 Posted: 26 Feb 2003 10:57 PST Expires: 28 Mar 2003 10:57 PST Question ID: 167425
 ```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.``` 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.``` 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).``` 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%``` 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.``` 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%```
 Subject: Re: financial calculation Answered By: nauster-ga on 02 Mar 2003 20:35 PST Rated:
 ```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```
 orte-ga rated this answer: ```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.```

 Subject: Re: financial calculation From: highroute-ga on 27 Feb 2003 07:40 PST
 ```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.```
 Subject: Re: financial calculation From: orte-ga on 28 Feb 2003 11:54 PST
 ```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.```