Talk:Reserve study

I am presenting the section below for review and updating. The nature for funding strategies should reflect the valuation of the common properties. I think the description of the straight line method is in error.

Funding methods and objectives

There are several reserve study funding methods and goals. These methods may be used to develop a funding strategy that corresponds with the risk tolerance of the community. In National reserve study Standards terminology, there are two basic funding Methods: "Cash Flow" or "Straight Line". Straight Line Funding models utilize a methodology in which funds are allocated to specific components, often not modeling the real world function of the reserve fund (where all Reserve Funds are available to be spent on all legitimate Reserve projects).

Dan (talk) 19:26, 16 July 2014 (UTC) (This is really what straight line is about) "Full funding" describes the objective to have reserves on hand equivalent to the value of the deterioration of the each reserve component. For example, for a $10,000 (current cost) pool resurface project with a useful life of ten years, after two years, when the pool's surface has deteriorated 2/10 of $10,000, to be fully funded the association should have $2000 set aside for this component (and on and on again for each component). "Full funding" describes an objective where ongoing deterioration is offset by the proportional accumulation of cash.

All funding objectives are designed to meet exactly the same expenses outlined in the reserve component list. Thus the expenditures are identical, only the size of the reserve fund through the years is different. This means the size of reserve contributions between different reserve funding objectives is relatively small (typically only 10–15%).

They are in fact identical once the 'base line' is reached. More information is available here:

Thanks, Dan.

References

Both of the given references appear to be either inaccessible or gone.

The pool example uses straight line funding and ignores inflation. Algebra is not opinion: If (using the same example) the inflation rate of pool replacement is 2½% (and doesn't change), then if the pool replacement project would cost $10,000 in the study year, it will cost $10,000×1.025¹⁰=$12,801 and require a special assessment for $2,801 in the project year, cheating owners in the project year to benefit all previous owners to varying degrees. Proper use of cash-flow would assess $1,280.10 per year for 10 years, which would cheat early owners by varying amounts to benefit later owners by varying amounts (convert all assessments to constant dollars in any year, which is how currencies of different values are compared, to see the extent of the cheating). Properly inflated, the first year assessment would be $1,142.59 and the second year $1,171.15 (so $2,313.74 would be fully funded after 2 years, not $2,000, which would be 13.6% underfunded). If you keep multiplying the assessments by 1.025 each year, you will find that the sum of them in the project year will equal $12,801, and if you convert each year's assessment to constant dollars of any one year, you will find that they are always the same. For such small projects with short lives, using funds assessed for other projects might be invisible; but it will be paid back in inflation adjusted dollars...IF a board is following a properly prepared reserve study. For a major project, it won't be invisible, and the cheating/payback may be painfully unfair to some.

How can the purpose of a reserve study be "to develop a funding strategy that corresponds with the risk tolerance of the community"? A Reserve Specialist has no way of documenting or calculating a community's risk tolerance; how much a community believes it can afford to pay does not change how much it will have to pay; and "creative" schemes to avoid proper reserves funding are unfair or increase costs or both. Current reserve study methods can be shown to not work even in theory; and the goals (funding and otherwise) of a reserve study for a condominium association are only variable to the extent that the board of directors chooses to ignore them.

In addition to the facility- and project-related information a reserve study provides, a condominium board of directors requires two things: current percent funded at their current inflation rate (every association's rate is different) and annual assessment amounts required to fund all future projects at the current rate of inflation and to fairly distribute the costs of those projects among owners. The numbers are not matters of opinion; they should be calculated. It's up to the board of directors to decide what their risk tolerance is and if they want to accept it.

"Straight line funding" methods violate the rules of algebra, which are not matters of opinion. Only zero inflation is a straight line; and it is mathematically impossible to adjust a straight line analysis of a group of projects for inflation after-the-fact.

"Base line funding" uses cash flow, which assumes straight line funding of estimated future project costs. Because straight line funding cannot be adjusted for inflation after-the-fact, cash-flow financially cheats the past to benefit the future (or vice-versa), so its distribution of future expenses is inherently unfair (even to one owner). Another problem with cash flow — "all Reserve Funds" being "spent on all legitimate Reserve projects" without regard to how much was assessed for each particular project — comes with the risk of "robbing Peter to pay Paul", possibly without a plan to repay Peter.

To an accountant, a dollar assessed in 1990 is no different from a dollar assessed in 2020, when in fact (not opinion), at 3½% average inflation, the purchasing power of the average assessed 1990 dollar had 281% of the purchasing power of the 2020 dollar; so by 2020 every dollar contributed in 1990 had lost 64% of its purchasing power. Those past losses to inflation had to be equitably distributed among owners of all years; otherwise, some owners pay an unfair share of actual project costs.

If the inflation rate of a large, 50-year component is significantly greater than the average, and the inflation rate of other components are significantly less, then after 15 or 20 years, Reserves could look so large that a board of directors might be tempted to assess less, because they seem to have so much money to spend on current projects. If that happens, then as that major long-lived component's project approaches, owners and the board of directors may wonder why their reserve studies are recommending assessment increases (sometimes far) in excess of the community's average inflation rate. It's because the closer a project is to a reserve study that doesn't treat inflation properly, the more realistically its actual (i.e., inflated) cost effects required assessments. If the board of directors ignores that warning sign and does not increase assessments accordingly, a special assessment or an interest bearing loan will result. Either way, current owners will have been cheated to benefit earlier owners. In my experience, long-time owners who "benefit" the most from that cheating will be the loudest to complain when the money they thought they were cheating some future owners of is suddenly required of them as now current "future owners"...

70.161.18.166 (talk) 20:27, 30 October 2021 (UTC)

I'm not sure where you get the idea that 'straight line' does not account for inflation. Inflation can be applied to any method.

Just because inflation is left from the examples does not mean it can not be used. 'Future Value' would be the inflated cost in the future.

Response:

1. Inflation cannot be correctly applied to any method that doesn't calculate the effects of inflation properly or that doesn't comply with the laws of algebra. I found neither was done consistently, when I analyzed the mathematics of a reserve study. My later use of the Percent Funded calculations suggested by our state and included in reference 1, gave results "all over the map" but incorrect. I've analyzed documents you updated the links to (thank you), and now better understand why the recommended Percent Funded equations don't work.

2. The first document implies lack of understanding of how to determine a funding level at the current rate(s) of inflation, and of the difference between interest and inflation.

3. On the first page of the first document, 5th paragraph: "If after the second pass on there are remaining funds then just the components being replaced are iterated and distribution is set to twice the replacement value.", which components being replaced are meant by "just the components being replaced"?

4. That page describes creating a plan for distributing the funds available through the study year until future projects cannot be funded at their current cost, adding annual contributions and interest, and repeating the process until the plan shows all projects funded at their current cost; after which any funds remaining are assumed excess. Because inflation is not properly addressed, all one need do is use properly inflated project costs for different components to show that neither assumption is necessarily correct.

5. Equation (1), on the second page, calculates the "future value" of "annuities due" as the sum in future year dollars (for the U.S. only), of the amount that will accrue at an interest rate over the term of the annuity, assuming interest accrues on contributions at the beginning of the year in which they are made. But a reserves account is not an annuity due that grows at an inflation rate; inflation decreases the value (purchasing power) of accrued contributions (always at the end of the year) and of interest in the next year. Mathematically, inflation is inverse interest (5% interest multiplies by 1.05^years; 5% inflation divides by 1.05^years), so the annuity equations are being misused, and the "future values" in all 3 equations are not valid future values of reserves.

6. The equations on page 4 may reflect what some people would like fully funded to mean, but by definition, fully funded means that when a project is due, sufficient funds have been accrued to pay for that project at its appropriately inflated cost. Before a project is due, "fully funded" may be defined by whoever is deciding to fund the project, but there is only one way measure the percent funded of multiple projects so that the value of the funds assessed through the year in which percent funded is calculated for any project is equal to the project age (or phase) divided by the project life (or phase interval), regardless of the project year; and that can achieved by a properly inflated component analysis and is not achieved by any other method I've seen.

7. The second to last sentence on page 4 calculates a constant payment for the life of the project, and since it doesn't correct for inflation, it will not account for prior assessments for any component that have lost value through the study year.

8. The graph on page 5 shows 3 graphs, of which only the one labeled "Assigned" represents fully funded, but only at 0% inflation. Until reserve studies can tell associations their real funding levels at the inflation of their association (which can be easily calculated from past and current study scope and unit cost data), the recommended annual assessments they provide can't theoretically accomplish the 3 main purposes of a reserve study (fairly distribute costs, avoid special assessments, and determine adequacy of past funding). This is why I approached my state on the subject: we are required to have reserve studies performed, but although we are not required to follow our reserve studies, if we do, they can't mathematically do what they're supposed to.

9. As for the second document, a Funding Strategy that doesn't attempt to properly distribute costs among owners in different years is easily shown to be unfair, and a strategy that doesn't properly calculate percent funding is not a strategy for funding, it's a strategy for cheating the future to benefit the past. Incompetent boards of directors don't need a strategy for that, they can just not fund reserves.

10. When I first reported the problems with reserve study calculations to FAI (Facilities Advisors International), I was told "current owners shouldn't have to pay for future inflation"; but that mathematically requires that "future owners pay for losses to inflation of funds contributed by past owners". Either way, that cheats future owners to benefit current owners; and since that can only be theoretically avoided by accounting for inflation properly, currently used methods can be shown, by converting recommended assessments constant dollars, to under-assess current owners and over-assess future owners.

11. Economists understand inflation because it's important to economics. Accountants don't need to; because to accounting, dollars are equal once they can be accounted for, and because customers that are not obliged to consider the fairness of how they collect their funding are not interested in fair distribution of costs among multiple owners.

70.161.18.166 (talk) 03:06, 4 November 2021 (UTC)

I won't address the first two paragraphs as they are vague claims without reference or meaningful content. Hand waving doesn't get it.

Third paragraph, you are citing from a section clearly presented as, 'At the start of the study.' So it follows that it refers to components that are being replace in the first year.

Fourth paragraph, you talk about inflation, this has nothing to do with distribution at the beginning of the year.

Fifth paragraph, baffling. The math is right out of any financial text book. Future value is a given.

Sixth paragraph, you don't understand 'Annuity Due Fully Funded'?

Seventh paragraph, patently false. Show your math.

Eighth paragraph, again, false. The calculation is based on 'future cost', hence, inflation is accounted for.

Ninth paragraph, you write, 'distribute costs among owners'. What does this mean?

Tenth paragraph, I'm not privy to your conversation with FAI.

Eleventh paragraph, pretty broad claim and has nothing to do with my documents. I clearly consider inflation. You have shown no math, but you rant a lot. — Preceding unsigned comment added by Lakeweb (talk • contribs) 16:33, 6 November 2021 (UTC)

Response:

12. I have gone back and numbered my previous paragraphs to make it easier to follow yours. By ranting, you appear to mean making claims unsupported by calculations and reasons you agree with, yet the document "explaining" Percent Funded doesn't explain distribution well enough for someone else to reproduce it in a spreadsheet or a program; and it doesn't explain how it gets from Distribution to the assumption that annuity calculations apply to reserves. Wikipedia wants references; but if a reference exists that doesn't espouse the methods of the people who claim to have "written the book" on reserve studies (https://www.google.com/search?channel=fs&client=ubuntu&q=%22we+wrote+the+book%22+reserve+study), it's not to be found on the Internet. As Wikipedia has pointed out more politely, the Reserve Studies page uses only references created by the people who claim to have written the book on the subject. No-one seems to know who verified that the people who "wrote the book" knew what they were doing.

13. Regarding your 4th comment (on my 5th paragraph), mathematically, an annuity to which spreadsheet FV and RATE functions may be applied is an investment funded by equal periodic payments over the funding period of the annuity. The rate of an annuity is the expected (or required) rate of return on those periodic equal investments. So equating the desired "future value" of reserves to the "future value" of an annuity, mathematically assumes that a constant (not inflated) amount is contributed to reserves every period, and then earns a rate of return determined by trial-and-error to give the desired "future value". Instead of investing the constant payments in an investment with that rate of return, the required earnings then become a surcharge to the people contributing the constant payments. Since rates of return do not give linear results, owners every year must pay more surcharge every year, even though the benefit they receive from the component every year does not change. To summarize, owners are asked to contribute to an investment that has a rate of return higher than the inflation rate, and are then required to fund its gains. Sounds like a shady investment. Please explain the benefit of asking owners to do that over asking owners to fund a future project by contributing to a savings account (which a reserves fund is) without regard to the benefit they are getting from the components they're paying for their use of, by funding their future replacement.

14. Since the laws of algebra are not subject to opinion, references are irrelevant to proving something mathematically. You claim to want numbers, so I'll start below with the "way to do it correctly", provided to me in 2016 by the organization that claims to have written the book on reserve studies. I'm not familiar enough with the modified HTML used by Wikipedia to make the table look identical to the original, but the layout, numbers and labels are identical. I even flagged the rounding errors in red so you know I know they exist. The sheet did not come with an explanation of whether year 1 is the study year or the first year of assessments, but although there was no explanation of "Constant Equal", I recognize it as the proper cash-flow assessments required to fund a $17,758 project; so year 1 must be the year after the study year. That means that the project costs are incorrect, because a year of inflation is missing; the project cost in year 30 would be $10,1000*(1.02^30)=$18,114 (added 12/4/21: or the project cost in the study year would have been $10,1000/1.02=$9,804). The "Constant Equal" assessments would slightly under-fund the project, distributing the inflated project dollars (price) equally among years, but distributing the value of those dollars unfairly, favoring later owners (whose dollars have less value/purchasing power) over current/early owners (whose dollars have more value/purchasing power). Although the "Constant Equal" column would be a correct use of cash flow at $18,114/30=$604 per year, the values in it are not used for anything by the rest of the table.

15. The "Assessment Factor" was the biggest puzzle, because the fairest distribution of the purchasing power of project costs would inflate at the inflation rate, which is already known. I figured out that the beginning assessment of $333 was $10,000/30 (much too low, hence the need for a large fudge factor disguised to sound legitimate with the name "Assessment Factor"), and that subsequent assessments appeared to be inflated by the "Assessment Factor", though not very accurately. So, using trial and error, I found that 1.036909 gave results that eliminated the inaccuracies, including the difference between cumulative assessments and the year 30 project cost. After our above discussions of annuities, I tried calculating the "Assessment Factor" using the Excel RATE function for a normal annuity, the result (1.0369093235565377) proves that the idea of annuities being related to reserves isn't confined to Percent Funded equations.

16. Referring to the dollars under the "Owner 1" and "Owner 2" columns: to an accountant, an owner during the first 15 years will pay ($6,521/$11,246)-1=58% of what an owner in the second 15 years will pay. In purchasing power, that number is 78% (based on constant dollars or hours to earn, one of which you should be able to calculate without my instruction). The cash flow assessments would result in an owner in the second 15 years paying 74% of the purchasing power an owner in the first 15 years would pay, even though the dollar amounts they pay would be identical. So by using the "Assessment Factor", the people who "wrote the book" are just reversing who (on average) gets cheated at the expense of whom. I suppose cheating the people who aren't yet there to defend themselves, to benefit people who are there now and would bitterly complain if they were the ones being cheated, would be the choice of crooked boards and owners. The fairest assessments would begin with $446.50 in year 1 and increase by a factor of 1.02 thru year 30. Those numbers increase at exactly the inflation rate, favor neither early nor late owners, and can be used to determine the required past funding for the project to be 100% funded as of the study year if the previous project had been built less than its useful life prior to the study and were therefore expected in less than it's useful life.

Example:

• If the last project were in study year minus 5, the component would be 5 years old in this study year.
• At the current inflation rate that project's study year price would have been $10,000/(1.02^5)=$9,057.30.
• The future price (now year 25) would have been (and still is) $9,057.30*1.02^30=$16,406
• The past 5 years' assessments would have been $404.41+$412.50+$420.75+$429.16+$437.75=$2,104.57, meaning $2,104.57/$16,406=12.8% in replacement reserves for this component in the current study year would be fully funded, and...
• The current year 1 assessment would still be $437.75*1.02=$446.50).
• Initial assessments can be determined by trial and error, or...
• To be exact: where "A" is the year 1 assessment, "I" is the inflation factor, "C" is the inflated project year cost, and "n" is the useful life, A=C×I/(I+I²+...+Iⁿ).
• Should you find errors in my calculations, I would appreciate being informed so I can correct them.

	Inflation Factor 1.020				Assessment Factor 1.037
	Inflated     Cost		Assessments				Constant     Equal
Year			Owner 1	Owner 2	Combined				Cumulative	%
1	$ 10,000		$ 333		$ 333		$ 592		$ 333	1.9%
2	$ 10,200		$ 345		$ 345		$ 592		$ 679	3.8%
3	$ 10,404		$ 358		$ 358		$ 592		$ 1,037	5.8%
4	$ 10,612		$ 371		$ 371		$ 592		$ 1,409	7.9%
5	$ 10,824		$ 385		$ 385		$ 592		$ 1,794	10.1%
6	$ 11,041		$ 399		$ 399		$ 592		$ 2,194	12.3%
7	$ 11,262		$ 414		$ 414		$ 592		$ 2,608	14.7%
8	$ 11,487		$ 430		$ 430		$ 592		$ 3,038	17.1%
9	$ 11,717		$ 445		$ 445		$ 592		$ 3,483	19.6%
10	$ 11,951		$ 462		$ 462		$ 592		$ 3,945	22.2%
11	$ 12,190		$ 479		$ 479		$ 592		$ 4,424	24.9%
12	$ 12,434		$ 497		$ 497		$ 592		$ 4,921	27.7%
13	$ 12,682		$ 515		$ 515		$ 592		$ 5,436	30.6%
14	$ 12,936		$ 534		$ 534		$ 592		$ 5,970	33.6%
15	$ 13,195		$ 554		$ 554		$ 592		$ 6,523	36.7%
16	$ 13,459			$ 574	$ 574		$ 592		$ 7,097	40.0%
17	$ 13,728			$ 596	$ 596		$ 592		$ 7,693	43.3%
18	$ 14,002			$ 618	$ 618		$ 592		$ 8,310	46.8%
19	$ 14,282			$ 640	$ 640		$ 592		$ 8,950	50.4%
20	$ 14,568			$ 664	$ 664		$ 592		$ 9,613	54.1%
21	$ 14,859			$ 689	$ 689		$ 592		$ 10,302	58.0%
22	$ 15,157			$ 714	$ 714		$ 592		$ 11,015	62.0%
23	$ 15,460			$ 741	$ 741		$ 592		$ 11,755	66.2%
24	$ 15,769			$ 768	$ 768		$ 592		$ 12,522	70.5%
25	$ 16,084			$ 796	$ 796		$ 592		$ 13,318	75.0%
26	$ 16,406			$ 826	$ 826		$ 592		$ 14,143	79.7%
27	$ 16,734			$ 856	$ 856		$ 592		$ 14,998	84.5%
28	$ 17,069			$ 888	$ 888		$ 592		$ 15,885	89.5%
29	$ 17,410			$ 921	$ 921		$ 592		$ 16,804	94.7%
30	$ 17,758			$ 955	$ 955		$ 592		$ 17,758	100.1%
	$ 17,758		$ 6,521	$ 11,246	$ 17,767		$ 17,758
			$ 17,767

70.161.18.166 (talk) 02:18, 20 November 2021 (UTC)

Addition to previous response:

17. A response (without counter arguments) to my 4 Nov posts came 2 days later. I don't know if Wikipedia tracks or follows up on these talks, but two weeks [1/15/22 ― 2½ months] after providing equations and examples, there's still no response. My contacts with the people who claim to have "written the book" on Reserve Studies have been similar; they continued to maintain that constant dollars are not a valid measure of the fairness of assessments in different years...but have not responded since I sent proof of unfairness in terms of the hours required to earn those assessments in different years (assuming income inflates at the same rate as inflation). After the failed attempt with the above table, they have never provided mathematical or logically sound reasons rebutting any challenge to current Reserve Study methods.

18. The first sentence in the main article says "A reserve study is a long-term capital budget planning tool which identifies the current status of the reserve fund and a stable and equitable funding plan to offset ongoing deterioration, resulting in sufficient funds when those anticipated major common area expenditures actually occur." What I've highlighted in bold red are what a Reserve Study for any entity that needs to fairly distribute funding among different owners and years should provide. For any other purpose, a funding plan based on proper use of cash flow (i.e., assessments based on cash flow to cover inflated project year costs will suffice).

19. Studies can be done correctly by simply following the mathematically dictated requirements, and the results can be shown to mathematically and logically meet the requirements (to the extent possible under inflation, which is inherently inequitable); however, I am unable to find evidence that Reserve Studies meeting the requirements of a condominium association (etc.) are currently available anywhere. So how does one explain how to do something on Wikipedia for which no valid references exist? For over 30 years, a clueless Reserve Study industry has been selling studies that don't do what condominium associations require of them, because the customers are just as clueless; and because neither the customers nor the industry itself checks the results. There may even be condominium associations that have religiously followed their Reserve Studies and still required "special" assessments for known future requirements. Even states are consulting Reserve Specialists, who clearly have a conflict of interest in developing laws and recommendations affecting condominiums.

20. I recently began to mathematically "disassemble" my association's 2019 Reserve Study, and discovered what appears to be the actual use of the process referred to in the second sentence of my paragraph 12, above, saying I was unable "to reproduce...in a spreadsheet or a program". Our Study has more detail on the process, but still not enough to allow duplicating the results. However, no-where in the study can I find a purpose for the process, or evidence that any use is made of its results. It is part of the still-recommended "cash flow method" based on analysis of current year costs, it sets beginning assessments as study year costs divided by component life, and it inflates recommended assessments progressively thereafter, without explaining how or why and further biasing assessments in favor of current owners at the expense of future owners. Actual numbers: our study claims to use an inflation rate of 2.3% per year (too low, based on past vs study year costs), and inflates recommended assessments by 0%, 4.33%, 5.09% and 5.84% for years 1, 2, 3 and 4 after the study year, respectively. How those inflation rates are calculated is not shown, and a recommendation is not provided for year 5, even though studies are required every 5 years. Owners in year 4 have to work 8.4% longer (assuming pay inflates at 2.3% per year) than owners in year 1, to earn their "fair" share of annual assessments (and if pay doesn't inflate, higher initial assessments are necessary to avoid under-funding).

70.161.18.166 (talk) 16:36, 4 December 2021 (UTC)