# AustraliaDouble Declining Balance Question

#### marenello

So undertaking a bit of part time post grad study and basically a bit confused with the double-declining depreciation method.

I've looked around at examples, but haven't been able to find a suitable answer.

My question is for a given useful life of an asset to be depreciated, does the ending book value have to equal to residual value?

In all the examples I've seen, I understand you can't depreciate past book value, so in the final years, the depreciation is less than what the equation states, or even zero. I understand that scenario.

But how about if you don't actually reach book value (through the equation) during the useful life? In class, it was shown that you *can* simply, allocate a larger amount for the final year to reach the residual value, or alternatively, smooth out this amount over the final few years. However this seems to contradict with the examples I've seen online?

Anyone care to weigh in? Can provide an actual number example if required, but was hoping to not have to insert a table.

#### WeirdVibeInc

Generally I've seen people say that you have to make a giant step down to the salvage value in the last year. It doesn't make much sense to me. It seems like DB/DDB are a poor approximation of exponential decay, which is what people are actually trying to make it do.

#### Behrouz Aftabigilvan

So undertaking a bit of part time post grad study and basically a bit confused with the double-declining depreciation method.

I've looked around at examples, but haven't been able to find a suitable answer.

My question is for a given useful life of an asset to be depreciated, does the ending book value have to equal to residual value?

In all the examples I've seen, I understand you can't depreciate past book value, so in the final years, the depreciation is less than what the equation states, or even zero. I understand that scenario.

But how about if you don't actually reach book value (through the equation) during the useful life? In class, it was shown that you *can* simply, allocate a larger amount for the final year to reach the residual value, or alternatively, smooth out this amount over the final few years. However this seems to contradict with the examples I've seen online?

Anyone care to weigh in? Can provide an actual number example if required, but was hoping to not have to insert a table.
In accounting we have sth called change in accounting estimates which are to be applied prospectivelly. If for any reason like change in your usage intensity or maintenance routines, residual value would be different( imagine after thtee years you find this out), you need to recalculate everything for the remaining periods.
Other than this, your formula should result in similar book value and initially determined residual value at the end of the asset's useful life. If you could upload an example where it does not, I would be better able to help. Remember you can Excel to verify your calculations. (Behrouz Aftabigilvan).

If the finall book value ends up being different than the initial residual value

#### WeirdVibeInc

In accounting we have sth called change in accounting estimates which are to be applied prospectivelly. If for any reason like change in your usage intensity or maintenance routines, residual value would be different( imagine after thtee years you find this out), you need to recalculate everything for the remaining periods.
Other than this, your formula should result in similar book value and initially determined residual value at the end of the asset's useful life. If you could upload an example where it does not, I would be better able to help. Remember you can Excel to verify your calculations. (Behrouz Aftabigilvan).

If the finall book value ends up being different than the initial residual value
I'm not sure you completed your post. OK then, what is the formula for Declining Balance and for Double-Declining Balance that results in the final value at the end of life being the same as the salvage value? Plot that on a graph and see for yourself. DB and DDB don't make any sense. The intent is to do exponential decay, but it's like the accountants who came up with that didn't understand that concept, and hacked this weird approximation that doesn't accomplish what they say it does. Not only that, but it seems like every other website I find that describes it has a different formula. Some of them don't produce any meaningful results at all.

Last edited:

#### WeirdVibeInc

Related post: https://www.accountantforums.com/threads/declinining-balance-depreciation-and-salvage-value.150085/

Related study with regard to technology depreciation: https://www.federalreserve.gov/pubs/feds/2004/200431/200431pap.pdf

... which states:

"Under current tax rules (the “Modified Accelerated Cost Recovery System”), PCs and other types of computing equipment are depreciated over a five-year period. The annual deductions are calculated using the “double-declining-balance” (DDB) method with a switch to the straight-line method at the point that maximizes the present value of the deductions. The double-declining-balance method specifies an annual percentage deduction that is twice the straight-line rate. For an asset with a five-year recovery period, the DDB deduction rate would be 40 percent annually."

So the "accepted rules" still fall off a cliff when DDB hits the straight-line plot, which makes calculation difficult.

(I'm writing a script with the python piecash abstraction of the GnuCash bindings to calculate accumulated depreciation for all my assets, which is why I'm trying to figure out how to do it right.)

#### DrStrangeLove

VIP Member
I'm not sure you completed your post. OK then, what is the formula for Declining Balance and for Double-Declining Balance that results in the final value at the end of life being the same as the salvage value? Plot that on a graph and see for yourself. DB and DDB don't make any sense. The intent is to do exponential decay, but it's like the accountants who came up with that didn't understand that concept, and hacked this weird approximation that doesn't accomplish what they say it does. Not only that, but it seems like every other website I find that describes it has a different formula. Some of them don't produce any meaningful results at all.
The intent is to do geometric decay, not exponential. The two are close, but not the same.

If you compare how the depreciable amount (cost value less salvage value) changes over the depreciation period T by various methods, you'll see they all start at the same point (cost less salvage value, 0) and all end at the same point (0,T). Mathematically, you're traversing the square {(0,0), (0, T), (cost less salvage value, 0), (cost less salvage value, T)} from the upper left corner to the lower right corner below the straight-line segment from (cost less salvage value, 0) to (0, T). And there are a LOT of paths between those two points in that region, all of which represent allowable depreciation schedules. For ease of implementation's sake, there are only a few used, k% declining balance being a set of them.

And for financial/economic reasons, there's a floor at the salvage value. So at some point there's a step down to salvage value that makes the tail of the curve go klunk.

#### Behrouz Aftabigilvan

I'm not sure you completed your post. OK then, what is the formula for Declining Balance and for Double-Declining Balance that results in the final value at the end of life being the same as the salvage value? Plot that on a graph and see for yourself. DB and DDB don't make any sense. The intent is to do exponential decay, but it's like the accountants who came up with that didn't understand that concept, and hacked this weird approximation that doesn't accomplish what they say it does. Not only that, but it seems like every other website I find that describes it has a different formula. Some of them don't produce any meaningful results at all.

I couldn't attach an Excel file here but uploaded the google drive link below.

The reason why calculations do not add up lies in calculation of the RATE you use. The right formula is

Rate=1- (Salvage Value/Cost)°(1/useful life).

° means TO THE POWER OF.

First years dep: Cost* Rate
Following years' dep: (cost- total of previous years depreciations)* rate or ( book value*rate).

Hope this will help you.

#### Behrouz Aftabigilvan

I'm not sure you completed your post. OK then, what is the formula for Declining Balance and for Double-Declining Balance that results in the final value at the end of life being the same as the salvage value? Plot that on a graph and see for yourself. DB and DDB don't make any sense. The intent is to do exponential decay, but it's like the accountants who came up with that didn't understand that concept, and hacked this weird approximation that doesn't accomplish what they say it does. Not only that, but it seems like every other website I find that describes it has a different formula. Some of them don't produce any meaningful results at all.
I guess the actual formulas for US are all here: https://www.irs.gov/pub/irs-pdf/p946.pdf

Horse's mouth... and you can depreciate that too
Well, I just had a look. The point is that in accounting we have depreciation prepared for accounting purposes and depreciation for tax purposes. Tax authorities do not accept the depreciation that companies calculate based on their own reasoning. Instead they provide some formulas and only the Depreciation calculated that way would be tax deductible. The difference between the two will result in tax asset or tax liability in financial statements.

Remember that the formula and rates determined by Tax authorities do NOT include any residual value. From their perspective residual value would be zero after 3,4,5 year whatever they say in their tables for different asset classes. However in your financial statements you can calculate depreciation and assume that your asset will have a residual value.
When there is no residual value, the rate would
be 1÷useful life. × (200% or 150% or...)

I reckon the confusion has arison because you have tried to combine both depreciations.
There are TWO depreciation figures: one that reflect your company's use and ends up in your financial statement and one that will be used when calculating amount of tax payable in your tax return.

I can provide you with an example if this doesn't ring a bell.

(Behrouz Aftabigilvan)

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