Why Oracle design the formula like this? It looks far different than the requirement description.(See extracted requirement in below passage)
For formula itself, it can be explained easily.
Guarantee depreciation amount can be calculated as “Cost * Guarantee Rate”
Depreciation Rate before switching can be calculated as “Begin NBV*Original Rate”
Depreciation Rate after switching can be calculated as “NBV when switching*Revised Rate”
The formula can be explained easily as “When depreciation amount less than guarantee amount, we will switch the rate from original rate to revised rate.” And due to “Dual Rate Evaluation” depreciation basis rule, the depreciation basis is changed from NBV of each begin of fiscal year to the NBV of the asset as at the date of the switch from Original rate to the Revised rate. It means after switching rate to revised rate, it is straight line depreciation on the base of the NBV of the asset as at the date of the switch from Original rate to the Revised rate.
The formula is explained, but the formula looks far away from requirement description! Why? And how the figure of revised rate and guarantee rate get from? Is it given by government? NO! It is introduced to design formula. The requirement has not any place mentioned these kind of rate.
Requirement
The Old Declining Balance Method is calculated by multiplying the book value as of the beginning of the fiscal year by a predetermined depreciation rate. The New Declining Balance Method will be calculated by multiplying the book value as of the beginning of the fiscal year by the depreciation rate, which is 2.5 times the depreciation rate under the straight line method. If the amount calculated using the New Declining Balance Method is less than the “amount calculated by dividing the book value as of the beginning of the fiscal year by the remaining years (useful life less the elapsed year)”, then the calculation method will be changed from the declining balance method to the straight line method when calculating the depreciation limit.
It is decided on a fiscal year basis whether the “amount calculated by multiplying the book value as of the beginning of the fiscal year by the depreciation rate which is 2.5 times the depreciation rate under the straight line method” is lower than the “amount calculated by dividing the book value as of the beginning of the fiscal year by the remaining years”. A change of method from the declining balance method to the straight line method in the middle of a fiscal year is not permitted.
Let’s have a look at how revised rate and guarantee rate is gotten.
From requirement description,
Assuming asset cost = a, depreciation year = b, original rate=x, so, there’s a relationship b=1/x*2.5
So, by original rate declining balance deprecation in the first years,
Year |
Depreciation Value |
NBV |
1 |
xa |
(1-x)a |
2 |
x(1-x)a |
(1-x)^{2}a |
3 |
X(1-x)^{2}a |
(1-x)^{3}a |
… |
… |
… |
n |
X(1-x)^{n-1}a |
(1-x)^{n}a |
… |
… |
… |
Against the requirement, If the amount calculated using the New Declining Balance Method is less than the “amount calculated by dividing the book value as of the beginning of the fiscal year by the remaining years (useful life less the elapsed year)”, then the calculation method will be changed from the declining balance method to the straight line method when calculating the depreciation limit.,
We can get a inequation as below, assuming n is the switching year
x(1-x)^{n-1}a<(1-x)^{n-1}/(b-(n-1))a (b=1/x*2.5)
On the base of total deprecation year, we can get the switch year.
For example, b=10, x=0.25 in above screendump,
Finally, we can get n>7 from above inequation. So, at the eighth year, we need to switch from the declining balance method to the straight line method when calculating the depreciation limit.
On the base of n=8, we can calculate so-called guarantee rate to help design the formula.
Guarantee Rate = right of inequation = (1-x)^{n-1}/(b-(n-1)) = 0.75^{7}/3 = 0.0445!
Revised Rate = 1/(b-(n-1))=1/3=0.33
As similar as above you can calculate the guarantee rate and revised rate for depreciation year 5, 10, 20 or others.
For this case, switching year n can be calculated as 14 by inequation.
Guarantee Rate = 0.875^13/7=0..252
Revised Rate = 1/7=0.143
Can you understand it now? Is it interesting? And who designed this formula?