Depreciation

[Robert Uhl <ruhl at 4dv.net>]

Michael Edwards <xg2 at onearmedman.com> writes:
>
> It's not terribly serious, I'm just idly trying to figure out how to
> calculate it on some of the pricier office equipment after having
> moved them from an expense to an asset.

Well, there are various methods of calculating depreciation.  The best
is to subtract current market value from the purchase price--but how do
you know what that current market value is?  For some goods one can find
out (e.g. Kelly Blue Book for cars), but for most one must guess.  A
first-order guess is to take the value of the object and divide by the
number of terms until it is worthless, then subtract that amount each
term.  E.g.:

  You have a $144 radio which you guess will be worthless at the end of
  three years.  You could do depreciation yearly, which means that at
  the end of each year you'd subtract $48 ($144/3 years = $48/year) from
  the value, or monthly, subtracting $4 ($144/36 months = $4/month), or
  whatever.

The problem with this is that it's not very realistic.  Most items start
out losing a lot of value, then slow down--the depreciation function is
a curve, not a line.  The sum-of-digits method approximates this and is
fairly easy to use.  What you do is divide the value by the sum of 1 to
the number of terms (1+2+...+n); call this x.  Then the first term you
subtract n*x; the second (n-1)*x; the third term (n-2)*x and so on.
This is actually easier than it looks: remember that the sum of all
numbers from 1 to n is n*(n+1)/2.  E.g.

  You have the same $144 radio.  You want to depreciate it over three
  years: 3*4/2 = 6.  $144/6 = $24.  At the end of year one you subtracte
  3*$24 = $72 (value = $72); at the end of the second year 2*$24 = $48
  (value = $24); at the end of the third year 1*$24 = $24 (value = $0).
  Maybe you'd rather do it monthly: 36*37/2 = 666; $144/666 = $.216.
  The first month you subtract 36*$.216 = $7.784 from $144 yielding
  $136.22.  The second month you subtract 35*$.216 = $7.560 from $136.22
  yielding $128.66, and so on.  You can see that each term the item
  depreciates by slightly less (in the final month it will lose only 22
  cents!); this is somewhat more realistic.

I use the sum-of-digits method for all of my assets save my car.  My
idea is that if I ever sell something I'll propose a price based on
simple depreciation (there are simple folks out there) and accept
anything above or at the sum-of-digits value.  I feel that it gives me a
better handle on my financial situation, and the added work is worth it.

GnuCash doesn't directly support sum-of-digits; what I do is use the
transaction to specify the bits I need.  E.g. one month it will read
`Depreciation (23 * .7894)'; the next month I know that I'll need to
multiply 22 by .7894.  GnuCash allows arithmetic expressions in the
debit and credit fields, so I simply credit 22*.7894 from the asset and
away I go.

-- 
Robert Uhl <ruhl at 4dv.net>
Youth is a blunder, manhood a struggle, old age a regret.
                                     --Benjamin Disraeli