- Compute the annual depreciation
Take the product of the depreciation charge per depreciation unit and the annual depreci-
ation units. Or, D 1 = $2.40(4000) = $9600; likewise, D 2 = $11,400; D 3 = $8100; D 4 =
$4500; D 5 = $3600. Taking the sum of these charges, we see that the total depreciation =
$37,200.
SUM-OF-THE-DIGITS METHOD
OF DEPRECIATION
A machine costing $15,000 is expected to remain serviceable for 7 years. The machine
will have a salvage value of $1000. What are the annual depreciation charges based on the
sum-of-the-digits method?
Calculation Procedure:
- Compute the machine wearing value
The wearing value W, or total depreciation = $15,000 - $1000 = $14,000. - Compute the annual depreciation
Use the relation Dv = W(N- U+ 1)/0.5 [#(#+ I)], where U= year number. Thus, for U=
1, D 1 - $3500. Likewise, for U= 2, D 2 = $3000; for U= 3, D 3 = $2500; for U= 4, D 4 =
$2000; for U= 5, D 5 = $1500; for U= 6, D 6 = $1000; for U= 7, D 1 = $500.
COMBINATION OF TIME- AND
USE-DEPRECIATION METHODS
A machine cost $38,000 and has a life of 5 years and a salvage value of $800. Studies
show that one-third of the total depreciation stems from the effects of time and two-thirds
stems from use. Compute the annual depreciation charges if time depreciation is based on
sum of the digits and use depreciation on a production basis with all units of equal quali-
ty. Use the same production as in the third previous procedure.
Calculation Procedure:- Divide the wearing value into its two elements
Knowing the respective depreciation proportions, let the subscripts t and u refer to time
and use, respectively. Also, W = $38,000 - $800 = $37,200, and Wt = ^($37,200) =
$12,400; Wu =^2 / 3 ($37,200) = $24,800. - Compute the annual depreciation charge
For the first year, Dn = W 1 NI[N(N + 1/2] = $12,400(5)/[5(6/2)] - $4133. Also, Dul =
($24,800/10,000 units)(2000 units the first year) = $4960. Thus, the total depreciation for
the first year is D 1 = $4133 + $4960 = $9093.