20210326INT to Staff Attachment 1_Calculation Explanation.docx

CALCULATION OF THE “CALCULATED ACCUMULATED DEPRECIATION” VALUE
The detailed depreciation calculations as presented in Section 8 of the Concentric report include the Calculated Accumulated Depreciation amount. The calculated accumulated depreciation amount is determined by multiplying a Calculated Accumulated Depreciation ratio (CAD ratio) by the original surviving cost of each vintage, as adjusted for a mid year rule of installation and by the Net Salvage Factor.
The CAD ratio is determined for each vintage based on the age of the vintage as at the study date, through the algorithms within the Concentric software based on the solutions to the Iowa curves as published by the Iowa State University by Robert Winfrey in Bulletin 125 (published in 1935), and as updated in Iowa State Bulletin 155, (published in 1935). The procedure to calculate the CAD ratio is more generally described in the textbook “Depreciation Systems” by Frank K. Wolf and W. Chester Fitch, published in 1994, beginning at page 84.
The Depreciation Systems text also provides solutions to the Iowa curves, beginning at page 308. The solutions to the tables as published in Depreciation systems, have been tested and conform to the solutions as used in the Concentric software for all age intervals where the age interval, (when expressed as a percentage of the average service life) is a whole percentage. The Concentric programs use a solution to the original formula to solve for age intervals that are a fraction of a whole percentage. For example, for a vintage that is 14.5 years old (giving recognition to the half-year rule), with an expected average service life of 58 years, the age as a percentage of average service life would indicate an age of 25.0% of the expected life. In this circumstance the Concentric solution for the CAD ratio will be between the ratios related to 25.0% and 26.0% as published in the Depreciations system text.
Once the CAD ratio is determined the Calculated Accumulated Depreciation Amount is equal to:
(Original Cost X CAD ratio) X the net salvage factor
The following example relating to account 367.0, Installation Year 2005 (page 8-13 of the Concentric report) is provided to further explain the calculations:
Given:
Calculations:
Age as at December 31, 2019 = 14.5 years, after adjustment for ½-year rule
age as a percentage of average service life = 14.5/58
0.25
CAD –25.0% of average life (page 326 of Depreciation systems textbook)
0.2408
0.2408 X $1,855,157.47
$446,721.92
adjust for net salvage = $446,721.92 x 135%
$603,074.59
The difference between the above calculated accumulated depreciation of $603,075 and the $603,144 results from the Concentric calculations,are due to rounding inherent in the CAD factor going to 4 decimal places in the Depreciation Systems textbook.
The “Depreciation Systems” and Iowa State Bulletin’s 125 and 155 are available for purchase through the Society of Depreciation Professionals (SDP), and are copywrite protected. Therefore, photocopies of the applicable pages are not provided with this response.
In order to avoid mis-understanding, Concentric notes that the “Accumulated Depreciation Factor” column provided in the detailed calculations in Section 8 of the Concentric report indicates the actual booked accumulated position as compared to the theoretical (or calculated) accumulated depreciation position as described above. The Accumulated Depreciation Factor as shown is the percentage of the Allocated Actual Booked Depreciation as a percentage of the original cost.