Depreciation.

[Slaine]

I have a value that depreciates monthly by a fixed percentage. My understanding (and this is all based on remembering my highschool maths lessons) is that to calculate the future value I would use the formula:

fv = pv * (1 - (r/12))^p

where:

fv = future value
pv = present value
r = annual rate
p = monthly period

I have done some sample calculations in excel and this appears to work.

Now the problem is I am maintaining a program that calculates it as follows:

fv = pv * (1 + (r/12))^-p

Again doing some calcs in excel shows that this gives slightly different values.

Can anyone hazard a guess as to what the program is actually doing? Is it some form of fancy depreciation?

All help/opinions appreciated.

[Guv]

You probably need a CPA to answer this one.

Your first formula obviously calculates what an asset is worth if it is diminished by a fixed percentage each period (month in this case).

The second formula seems to be the reciprocal of the compund interest formula. It is reasonable for a depreciation formula, but does not fit the common notion of what depreciation is.

I happen to remember that for income tax deductions and other accounting purposes, there are several different formulae, all of which do the job. Some of these do not seem to conform to any common notion of what depreciation is.

[beachbum]

Yeah there are a zillion forms of depreciation such as Diminishing Value Method, Prime Cost Method, Sum of Digits etc

Usually, the trap that ppl fall into with depreciation calculations is that it is based on a fixed financial year and so the monthly value is 1/12 th of the yearly calc.

Eg..
$1000 @ 12% over 12 months
Doing it by Year: Each month is $10 = $120
Doing it Monthly: $10, $9.90, $9.80 etc

I'm not sure how Excel does it as I dont have Excel on this machine but could check later on the other machine if this isnt your problem.

Regards
Stuart

[Jethro]

Reverse of calculating compound interest dude....

The depreciated amount per month should be deducted before calucating the next months value. Unless of course you are going the fixed depreciation to zero method, which will created problems down the line in accounting terms when you revalue the asset, unless of course you are disposing of the asset at the end of the fixed depreciation term.....

Had to check Stu....you have escaped from Chit Chat l see....

Slaine

Which method are you using, makes a whole lot of difference in the formula....

[beachbum]

Originally posted by Jethro
The depreciated amount per month should be deducted before calucating the next months value.

That is exactly what I was saying not to do ! Depn is usually for tax or accounting and is based on a full financial year adjusted for the relevant viewing period. I mean that if u depreciate an asset by $1200 in a full year then the six monthly figure is $600 and not a reduced number based on the calc of individual months.... damn someone might see me in here... better run...

[Lee_Truss]

Hey there,

Im sure I have got it in my BS notes that depreciation cannot be used for Tax purposes as it can be "fixed so to speak"

[Guv]

Lee_Truss: If you find it in your notes, your notes are incorrect. A business can take deductions for depreciation of capital assets. An individual can do the same if he reports rentall income on a property.

In the USA, the IRS has some regulations about the allowable formulae. Only certain assets can be depreciated to zero. If you do depreciate to zero for certain assets and then sell them you pay income on the proceeds of the sales. If you sell depreciated real estate, you pay income tax if you sell it for more than the depreciated value, but this is one you can almost always get away with not reporting. Better yet, take some of the sale price in cash.

Jethro:The depreciation formula originally shown is a predictive formula.

fv = pv * (1 - (r/12))^p

It tells you the depreciated value in advance for each period. There is no need to do subtractions before apply this formula. In a general ledger accounting system you are likely to have a monthly ledger entry for the depreciation which gets subtracted from the value of the capital asset recorded elsewhere. In this case, you do not use the formula at all. You merely calculate the depreciation for the current month

Depreciation = CurrentValue*r/12
NewValue = CurrentValue - Depreciation

If you keep your books normally, the original formula is merely used to predict what the asset value will be.

Others: After thinking about it for a while, the reciprocal of the compound interest formula seems like a reasonable formula.

[Lee_Truss]

Hey there,

This is coming straight from notes which I took of the whiteboard where I stood and watched my lecturer write it.

Depreciation is NOT allowed for tax purposes, but different fixed assets attract different capital allowances.

It might be because I live in the uk though.

[beachbum]

Capital allowance is basically another term for depreciation. This is what normally happens....

Companies use their own depreciation rates and methods to best provide useful management reports.

When they do their tax return they add back the 'book' rates of depreciation and then deduct the allowable tax rates.

So, say u had only one $1000 asset that u depreciated at 10% and the tax rate was 5% u might do something like this

Net Profit before Tax 3,000

Add back Book Depn 100

Deduct Tax Depn (50)

Profit for Tax Purposes 3,050

NB there are quite a few other Tax vs Normal profit adjustments besides depreciation.

[Slaine]

MMM seems like a can of worms has been opened.

This has nothing to do with Tax, but is instead part of a calculation of contract hire.

Greatly simplyfied the customer might be charged £10000 for a vehicle but the dealer gets a 1000 bonus for selling the vehicle.

The dealer passes on this bonus to the customer so they are only charged 9000.

The problem arises when the dealer doesn't immediatly recieve the bonus, they might have to wait 3 months for it. There fore the value of 1000 is reduced using the formula above. Using a fixed %.

So for example if there is a one month delay they might only pass back 900, for 2 months it might be 800 . . and so on.

Some examples

Bonus	 £10,000.00 		
Rate	10.50%		

                   pv * (1 - (r/12))^p       pv * (1 + (r/12))^-p
----------------------------------------------------------------------------------
Delay	1	 £991.25 	                     £991.33 
	2	 £982.58 	                     £982.73 
	3	 £973.98 	                     £974.20 
	4	 £965.46 	                     £965.75 
	5	 £957.01 	                     £957.38 
	6	 £948.64 	                     £949.07 
	7	 £940.33 	                     £940.84