SINKING
FUND DEPRECIATION
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, if 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 which
is covered elsewhere. 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 |
3
|
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.