FUTURE DEPRECIATION

The type of depreciation covered above is actual or historic depreciation which has affected the value of an existing building through accrued depreciation. However, the valuer in some methods of valuation and feasibility studies is required to make an estimate of the amount of expected depreciation a building will suffer in the future. There are four common models used for estimating the future accrued depreciation of a building:

 * STRAIGHT LINE
* REDUCING BALANCE
* SUM OF DIGITS
* SINKING FUND


STRAIGHT LINE MODEL

This is the simplest model. It assumes that the building will depreciate at a constant annual rate until the end of its life when, it will have zero value.
EXAMPLE Suppose that valuer expects that the building will have an economic life of 10 years and its replacement cost new is 2 000 000. According to this model the building will be worth 0 in 10 years at a depreciation rate of 10% per annum (200 000):

STRAIGHT LINE DEPRECIATION

YEAR
VALUE DEPRECIATION
0
2 000 000 200 000
1 800 000
200 000
2
1 600 000
200 000
3
1 400 000
200 000
4
1 200 000
200 000
5
1 000 000
200 000
6
800 000
200 000
7
600 000
200 000
8
400 000
200 000
200 000  200 000 
10
0
          

REDUCING BALANCE MODEL


In some circumstances a better model may be one that does not depreciate to zero at the end of the economic life of the building. For example, if it is expected that the depreciated building will have some value, such as a base for conversion to the new highest and best use. Under this model a constant annual amount of depreciation is not assumed but instead a fixed rate (eg 10%pa) of the REMAINING VALUE.

This is shown below:


REDUCING BALANCE DEPRECIATION


YEAR
VALUE
DEPRECIATION
2 000 000
200 000
1
1 800 000
180 000
2
1 620 000
162 000
3
1 458 000
145 800
4
1 312 200
131 220
5
1 180 980
118 098
6 1 062 882
106 288
7
956 594
95 659
860 934
86 093
9 774 841
77 484
10
697 357


SUM OF DIGITS MODEL

The sum of digits method increases the rate of depreciation over the economic life of the building and as with the straight line method, assumes a zero value at the end of the life. The formula is as follows:


SD = L/2(1 + L)

Where:
L = expected economic life.

For example, the sum of digits for a building with a 10 year life is: SD = 10/2 (1+10) = 55

The amount of depreciation for each year is the year number divided by the sum of digits.

EXAMPLE:

For year 5 the amount of depreciation will = 5/55 of the market value of the building at the start of that year. The resulting depreciation table is shown below:


SUM OF DIGITS DEPRECIATION 


YEAR VALUE  DEPRECIATION  FACTOR (year/55)
0
2 000 000
36 364 0
1 963 636
72 727
0.0182
2
1 890 909
109 091
0.0364
1 781 818
145 455
0.0545
4
1 636 364
181 818
0.0727
5
1 454 546
218 182
0.0909
1 236 364
254 546
0.1091
7
981 818
290 909
0.1273
8
690 909
327 273
0.1455
363 636
363 636
0.1636
10  0
0

        
SINKING FUND MODEL

 
The sinking fund model assumes that the owner of the building will invest an annual amount from the income of the building into a sinking fund (earning compound interest) so that at the end of the life of the building he/she will have the starting value of the building in the sinking fund. It assumes that the annual depreciation will equal the annual increase in the sinking fund and that the building will have zero value at the end of its economic life. The formula is as follows:

SFF = i/((1+i)n-1)

Where:

SFF = sinking fund factor

i = interest rate as a decimal

n = economic life

For the above example, we assume that the owner can invest the sinking fund contributions safely, at 10% per annum:

SFF = 0.10/((1.10)10-1) = 0.06275.


Therefore, the annual investment and depreciation amount:
0.06275 * 2 000 000 = 125 490 per annum This will accumulate to nearly 200 0000 over 10 years at 10% per annum. The value of the increasing fund is found with compound formula. The resulting table is as follows:

SINKING FUND DEPRECIATION


YEAR  VALUE  ACCRUED DEPRECIATION
0 2 000 000
1
1 874 509
125 491
2
1 736 469
263 531
1 584 626
415 375
4
1 417 597
582 403
5
1 233 866
766 134
6
1 031 762
968 238
7
809 447
1 190 553
8
564 901
1 435 099
9
295 901
1 704 099
10
0
2 000 000
            
For example, the accrued depreciation of the building at year 5 is 766 134. The amount of depreciation suffered during year 5 = 766 134 - 968 238 = 202 104. At the end of year 10, the full value of 2 000 000 has been lost leaving a building of zero value.

WHICH MODEL TO USE?


The best model is the one that will most likely correlate with the expected life of the subject building. In valuation practice, the most popular model is the sinking fund as it is compatible with the investment and compound interest theory used in the capitalization method of valuation. The valuer can determine the best model by deciding whether or not the subject building will have zero value at the end of its economic life and whether or not the rate of depreciation remains constant.
The depreciation models covered above illustrate the following important rules which relate to the value of improvements: The use of replacement cost new for old buildings can be most difficult. The older the building, the greater the variation between the current structure and the hypothetical structure that replaces it because:


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