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"Adequate Reserve" Formula
One of a variety of alternative formulas to estimate and quantify expenses for the purpose of determining reinvestment requirements. In other words a means of answering the question: "How much money will we need?" and therefore forms part of the financial analysis.


Parameters
A reserve balance that is sufficient to accommodate asset renewal projects for a period of "x" years (ie., a defined planning horizon). In some jurisdictions an adequate reserve is a reserve that is it at least 60% percent funded.


Adequate reserve is a performance-based target rather than a prescriptive-based target. Unfortunately, the term is open to interpretation based on different subjective opinions as to what constitutes "adequate".



Example
For example, a boiler replacement every 10 years (Frequency) at $10,000 (Current Value), escalated (at 2%) is $12,190, and should be funded at $1,219 per year.



Formula
This formula evaluates each renewal activity divided by either the frequency of the renewal activity or the length of the planning horizon, whichever is less, and also accounts for escalation. 
The following equation is used for each renewal occurrence.

∑ IF{EY > PH+BY,0,Costy / [IF(F > PH, PH, F)]}

         Where,

         Costy    Future Value of Renewal Event
         EY        Event Year, year of Renewal Occurrence
         BY        Base Year
         PH        Planning Horizon (30 Years)
         F           Frequency of the Renewal Activity

Similar to the Non-Termed formula, the following formula is used to determine the amount that should be in the reserve account at the base year.

∑ IF{EY > PH + BY, 0, (Costy / [IF(F > PH, PH, F)]) x ([IF(F > PH, PH, F)])  – (EY – BY))}

         Where,

         Costy    Future Value of Renewal Event
         EY        Event Year, year of Renewal Occurrence
         BY        Base Year
         PH        Planning Horizon, 30
         F           Frequency of the Renewal Activity

The combination of both equations provides the funding requirements moving forward (keep-up) and the unfunded liability looking backwards (catch-up). This model will fluctuate through the life of the building as capital renewal projects that are initially beyond-the-horizon come into the planning horizon.



Attributes and Parameters
The summary of funding attributes for this formula is provided in the table below
:
  • 1    Termed vs. Continuous    Termed (30 years)
  • 2    Inflated vs. Non-Inflated    Future Values (FV)
  • 3    Proximity v. Non-Proximity    Non-Proximity
  • 4    Linear vs. Lumpy    Linear
  • 5    Funding vs. Funded    Funding ($ per year)
  • 6    Catch-up Costs vs. Keep-up Costs    Keep-up and catch-up (two formulas)

Evaluation
Renewal activities with a frequency greater than 30 years may be included or excluded from the formula depending on whether the next renewal occurrence is inside or outside the planning horizon, which will depend on the age of the building.


This third method is preferred for the analysis as it respects a planning horizon and escalation.


Funding trajectories and inflection points resulting from three alternative funding methods - "Adequate Reserve", "Capital Load" and "Non-Termed.
Fig. Funding trajectories and inflection points resulting from three alternative funding methods - "Adequate Reserve", "Capital Load" and "Non-Termed.

See also:

Classes of Formulas
Reinvestment formulas can be grouped into three general categories, as follows:

Other Expense Quantification Formulas:

     
Group 1:
       Group 2: Compare with:


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