Students Enrolled in UBC Real Estate Division CPD 891: Fundamentals of Reserve Fund Planning

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1 BULLETIN 1 DATE: July 15, 2016 TO: RE: Students Enrolled in UBC Real Estate Division CPD 891: Fundamentals of Reserve Fund Planning Corrections to Course Materials The following clarifications are necessary in CPD 891. Where appropriate, the necessary changes have been highlighted in bold. PLEASE MAKE A NOTE OF THESE IN YOUR BOOKS NOW, IN ORDER TO AVOID CONFUSION LATER. COURSE WORKBOOK ASSIGNMENT Replace Question 18 with the following: 18. The following image is best described as: (1) Aluminum double glazed vertical sash window (2) Dual aluminum single glazed sliding window (3) Vinyl single pane vertical single hung window (4) Aluminum double glazed sliding door

2 UBC Real Estate Division Page 2 of 8 Formula Sheet for 891 Examination Future Replacement Cost (FRC): 1 CRC = Current replacement cost i = Inflation rate per annum n = Remaining lifespan in years Future Value for Replacement Costs: 1 PV = Present value of replacement cost i = Inflation rate per annum n = Remaining lifespan in years Current Reserve Fund Requirement (CRFR): CRC = Current replacement cost EA = Effective age in years NLS = Normal lifespan in years Future Reserve Fund Accumulation (FRFA): 1 CRFR = Current Reserve Fund Requirement j = Investment interest rate return per annum n = Remaining lifespan in years Future Reserve Fund Requirement (FRFR): FRC = Future replacement cost FRFA = Future reserve fund accumulation Annual Reserve Fund Accumulation Formulas (ARFA[x/y]) Level End of Period Payments (ARFA[level/end]): / Level Beginning of Period Payments (ARFA[level/beg]): Indexed End of Period Payments (ARFA[index/end]): / / Indexed Beginning of Period Payments (ARFA[index/beg]): / Where: j is the annual interest rate on investments g is the annual inflation rate for periodic contributions j g or the indexed AFRA formulas will be indeterminate due to division by zero n is the number of periods until the expiration of the useful life of the building element FRFR is the Future Reserve Fund Requirement Reserve Fund Adequacy Analysis: % CRFR = Current reserve fund requirement for the year under consideration

3 UBC Real Estate Division Page 3 of 8 ASSIGNMENT 3: Page 3.37 Revise Question 12 as follows: Which of the following statements regarding a component s life is TRUE? Revise options (3) and (4): Over-estimating a component s remaining life LESSON/ASSIGNMENT 4: Page 4.26 For the paragraph under Item: Roof replacement Modified Bitumen Single Ply, revise the second sentence as follows: This is calculated based on an expected cost of $3.64 per ft 2 a quality ranking of 2 (out of 4) for modified bitumen, single ply [$2.30+($6.80+$2.30)]/3, plus a $0.75 per ft 2 premium for removal and disposal. Page 4.27 For the paragraph under Item: Roof replacement Built Up Tar & Gravel, in the first sentence replace 12/3 with 1 ⅔. Page 4.28 For the paragraph under Item: Decking Access Stairs, in the second sentence, the reference plus a 10% premium for removal and disposal should be changed to plus a 15% premium for removal and disposal. In the table at the bottom of the page, the red rectangle that outlines should instead outline the numbers (for the item Siding, vinyl ). Page 4.34 In the table directly below the title Item: Carpet Stair Riser Flooring Replacement, the Replacement cost of $3.14 per ft 2 ($33.75 per m 2 ) should change to $2.71 per ft 2 ($29.17 per m 2 ). Similarly, in the paragraph directly below this table, in the first sentence the cost $3.14 per ft 2 ($33.75 per m 2 ) should be changed to $2.71 per ft 2 ($29.17 per m 2 ). The table at the bottom of page 4.34, labelled Floor Covering, should be replaced with the following table: Note the addition of staining at the bottom of the table.

4 UBC Real Estate Division Page 4 of 8 Page 4.36 The paragraph at the bottom of this page should be revised as follows: Cost of replacement is estimated to be $15.87 per ft 2 ($ per m 2 ). This is calculated based on a quality level of 3.5 (out of 4) with an expected cost of $9.14 per ft 2 five-sixths of the range from the lowest to highest cost in the range for concrete pavers on concrete base, less the same adjustment for sand base in place of concrete, or ($8.70+ [($14.40-$8.70) *5/6])-($2.54+[($4.66- $2.54)* 5/6]) plus a $2.25 per ft 2 cost for removal and disposal. Total cost is estimated to be $11.39 per ft 2 before adjustments. Toronto and Eastern regional adjustments increase the cost to $15.87 per ft 2 ($11.39 * 1.04 Eastern Region * 1.34 Toronto Class D) Section 66, Page 2. Page 4.41 Please make the following change to the table of information provided for Question 7 and 8: the Roof Element for building C should be changed from Built-up 2 ply to Built-up 3 ply. ASSIGNMENT 5: Page 5.9 The equation above the last paragraph, FRFS = $44,803 - $28,222, should be changed to FRFR = $44,803 - $28,222. Page 5.71 Change Option (1) in Question 12 to: (1) y = CRFR, x = ARFA, j = inflationary rate Page 5.72 The options for Question 18 should be changed to the following: (1) $572,891 (2) $468,784 (3) $481,942 (4) $471,855 PROJECT Project.2 Add the following under Project Submission : Once you have submitted your project to Turnitin.com, please notify your course tutor via that the project has been submitted. You can find your assigned course tutor s address on the Tutorial Assistance webpage. Please include your course name, last name, and student number in the subject line of your .

5 UBC Real Estate Division Page 5 of 8 Page Project.3, Project Requirements As referenced at the top of the page, the marks for each question should be changed from 20 marks each, to: Question 1: 25 marks Question 2: 20 marks Question 3: 25 marks Question 4: 10 marks Question 5: 20 marks Page Project.5 Add the following under Question 5(b): (iii) Assuming a 3% interest rate and 2.5% contribution inflation rate, calculate the annual contributions for an indexed model (assume payments remain paid at end of each year). How does this compare to an unindexed (level) contribution? LESSON 5: Page Lesson 5 presents calculations for determining the recommended reserve fund contribution for a condominium/strata. The technique illustrated on page is called the Component Method Funding Calculation, as it breaks down the overall contribution into the funding necessary to replace each individual item over the reserve fund timeframe. This Component Method applies a series of formulas to estimate the Annual Reserve Fund Assessment (ARFA) for each property element. The ARFA is the minimum contribution necessary for that element such that the future accumulation, with interest, will equal the element s Future Reserve Funding Requirement (FRFR). The application of this ARFA calculation is illustrated later in Lesson 5 in the Saskatchewan Condominiums and Kelowna Townhouses case studies. It is also the basis for the Fee Simple Commercial Property case study in the project at the end of the course workbook. 1 The ARFA formula on page 5.10 assumes that payments are made annually, at the end of each year, and are constant over the reserve fund study timeframe. These assumptions make ARFA simpler to calculate and understand, but each comes with drawbacks: 1. Annual payments in practice, owners will make monthly reserve fund contributions along with their monthly condominium/strata fees. The use of annual payments underestimates the interest accrued in the reserve fund. In contrast, using monthly contributions will account for the additional interest accrual that results from more frequent compounding. 2. Payments at end of period if the contributions were made at the start of each month or year, additional interest would accrue during that month or year. Assuming that payments are at the end of each month or year also underestimates interest accrued. 3. Constant payments it is easier mathematically to assume contributions will be the same every month or year over the reserve fund timeframe, but this means owners early in the timeframe will pay a greater real cost (inflation-adjusted) than owners in later years. In essence, this means that current owners are subsidizing the costs of future owners. 1 A second approach to estimating the reserve contribution is to program a cash flow analysis directly into a spreadsheet. Rather than using the ARFA formulas, the cash flows are calculated directly. When capital planning was initially introduced, it was time consuming and cumbersome to try to recalculate actual cash flows to determine an optimal contribution; the ARFA type calculations were seen as the only reasonable approach. With the development of spreadsheet programs, this is no longer the case and greater accuracy can be obtained with the cash flow approach. The cash flow technique is illustrated in the 55 Summer Lane case study.

6 UBC Real Estate Division Page 6 of 8 Of these three simplifying assumptions, the first and second may be reasonable. Using monthly payments will improve the model s accuracy slightly, but it may be questionable if this is sufficient to warrant the added complexity of the analysis keeping in mind we are analyzing a long-term future projection involving many uncertain assumptions. In this projection, there is a significant degree of estimating and guesswork involved, so there is only so much mathematical precision that is warranted in the calculations. (Although, if you are developing a spreadsheet and can easily address these issues, it is better to be more accurate than less!) However, the third assumption warrants more attention. Unitholders would naturally expect that contributions will increase over time, especially over a 25- or 30-year timeframe. Recommending a constant contribution over 25 or 30 years is an unrealistic simplification that should probably be addressed by the reserve fund planner. The ARFA formula presented on pages 5.10 assumes a level payment stream for the entire reserve timeframe and is based on contributions being received at the end of each period (months or years). The following section presents alternative formulas that deal with the assumptions for contribution growth (indexing) and beginning versus end of period payments. 2 End of Month Payment Beginning of Month Payment Level Payments ARFA[level/end] ARFA[level/beg] Indexed (Escalating) Payments ARFA[index/end] ARFA[index/beg] ARFA[level/end] This is the formula introduced on page It assumes that all payments are level/constant for the remaining useful life of each element; it also assumes that payments are not made until the end of a given period (meaning no interest is accrued for the contributions in a given year). The ARFA[level/end] formula is as follows: / 1 1 Where: j is the annual interest rate on investments n is the number of periods until the expiration of the useful life of the building element FRFR is the Future Reserve Fund Requirement For the roofing example on page 5.10, the ARFA[level/end] = $1,446 per year. This end of period payment with a level payment schedule is familiar to most real estate finance students as it is similar to the one used for calculating mortgage payments. It is easily performed using the functions on a typical financial calculator. In such a case, be sure that the payment is set to end of period before calculating the results. In calculating this in Excel with the PMT function, the Type is set to 0 to indicate an end of period annuity (or Type can be omitted, in which case Excel assumes end of period is the default). ARFA[level/beg] This alternative formula maintains the constant payments assumption, but considers the impact of payments made at the beginning of each period. This accounts for interest accrual over each month or year. For example, if an account had a balance of $1,000 on December 31 st of year 1 and an annual payment of $500 was made using the beginning of period criterion, then the interest calculation for year 2 is based on $1,500. The ARFA[level/beg] formula is as follows: 2 Note that the frequency of the calculation can be completed on an annual basis or a monthly basis for all of these formulas, just be sure to apply the appropriate periodic interest factor to ensure that you end up with the annualized effective inflation rate and interest rate to be used in the analysis. In the case of converting an annual interest rate to a monthly interest rate, use the following formula imth = [(1 + iannual) ^ (1 / 12)] 1. This can also be completed in Excel using the NOMINAL and EFFECT functions.

7 UBC Real Estate Division Page 7 of 8 / For the roofing example on page 5.10, the ARFA[level/beg] = $1,404 per year. It is logical that the contribution is lower than ARFA[level/end] because of the additional interest accruing during each of the ten years. This beginning of period payment with a level payment schedule is also familiar in lease analysis calculations, since rent is paid in advance. On a financial calculator, set the payments to beginning of period. In Excel s PMT function, the Type is set to 1 to indicate a beginning of period annuity. ARFA[index/end] The ARFA[index/end] formula assumes payments are made at the end of each period, but accounts for payments increasing at an annual rate of inflation (g). In this indexed scenario, if payments are rising at a rate of 2.0% per annum, the year 1 payment would be $ per year, the year 2 payment would be $ per year, the year 3 payment would be $104.04, and so on. The ARFA[index/end] formula is as follows: / 1 1 Where: j is the annual interest rate on investments g is the annual inflation rate for periodic contributions n is the number of periods until the expiration of the useful life of the building element FRFR is the Future Reserve Fund Requirement For the roofing example on page 5.10, the inflation rate g = 2.5%. The ARFA[index/end] = $1,299 per year 3. Again, it is logical that the contribution is lower, as it will increase every year over the 10 years, such that it accumulates exactly $16,581 at the end of this time. For example, the Year 2 payment is 2.5% higher at $1,331. The formula for the ARFA[index/end] is used to calculate a sinking fund payment in a Growing Annuity. Financial calculators are typically unable to provide this calculation, as the growth assumption is not normally programmed into them. However, you could verify this result by building a cash flow model in Excel. See the Excel document titled Student Calculation Sample Template ARFA under Online Readings and Videos, Lesson 5 on the course resources page for an example. ARFA[index/beg] The ARFA[index/beg] applies a growth rate to the payments and also assumes payments are received at the beginning of each period. / For the roofing example on page 5.10, the ARFA[index/end] = $1,261 per year 4. Again, it is logical that the required contribution is lower than the ARFA[index/end], as it now accounts for interest accrued during the year for each payment. 3 $16,581 x ( ) / ( ) 4 ($16,581 / (1.03) x ( ) / (

8 UBC Real Estate Division Page 8 of 8 Summary of Component Method Funding Calculations When calculating ARFA values, you must exercise caution when considering which formula to apply. Each will provide a different result and each may be more or less suitable in any particular scenario. In making this choice, it is important to keep the ultimate goal in mind: making a recommendation for the optimal funding contribution for unitholders in the condominium/strata. The choice of appropriate formula will depend on your opinion of the balance between added precision in the calculations and the usefulness of this in practice. As noted earlier, the differences between monthly versus annual or beginning contributions versus end of period contributions may be negligible, but indexed contributions are likely an important consideration. It is logical to assume that contributions would grow over time and it is practical to implement this in most real-life situations.