Depreciation
Depreciation is a systematic and rational process of distributing the cost
of tangible assets over the life of assets.
Depreciation is a process of allocation.
Cost to be allocated = acquisition cot - salvage value
Allocated over the estimated useful life of assets.
Allocation method should be systematic and rational.
Depreciation Methods
Depreciation methods based on time
Straight line method
Declining balance method
Sum-of-the-years'-digits method
Depreciation based on use (activity)
Straight Line Depreciation Method
Depreciation = (Cost - Residual value) / Useful life
[Example, Straight line depreciation]
On April 1, 2011, Company A purchased an equipment at the cost of $140,000. This
equipment is estimated to have 5 year useful life. At the end of the 5th year, the salvage
(residual value) will be $20,000. Company A recognizes depreciation to the nearest whol
month. Calculate the depreciation expenses for 2011, 2012 and 2013 using straight line
depreciation method.
Depreciation for 2011
= ($140,000 - $20,000) x 1/5 x 9/12 = $18,000
Depreciation for 2012
= ($140,000 - $20,000) x 1/5 x 12/12 = $24,000
Depreciation for 2013
= ($140,000 - $20,000) x 1/5 x 12/12 = $24,000
Declining Balance Depreciation Method
Depreciation = Book value x Depreciation rate
Book value = Cost - Accumulated depreciation
Depreciation rate for double declining balance method
= Straight line depreciation rate x 200%
Depreciation rate for 150% declining balance method
= Straight line depreciation rate x 150%
[Example, Double declining balance depreciation]
On April 1, 2011, Company A purchased an equipment at the cost of $140,000. This
equipment is estimated to have 5 year useful life. At the end of the 5th year, the salvage
(residual value) will be $20,000. Company A recognizes depreciation to the nearest whol
month. Calculate the depreciation expenses for 2011, 2012 and 2013 using double decli
balance depreciation method.
Useful life = 5 years --> Straight line depreciation rate = 1/5 = 20% per year
Depreciation rate for double declining balance method
= 20% x 200% = 20% x 2 = 40% per year
Depreciation for 2011
= $140,000 x 40% x 9/12 = $42,000
Depreciation for 2012
= ($140,000 - $42,000) x 40% x 12/12 = $39,200
Depreciation for 2013
= ($140,000 - $42,000 - $39,200) x 40% x 12/12 = $23,520
Double Declining Balance Depreciation Method
Book Value Depreciation Book Value at
Year Depreciation Rate
at the beginning Expense year-end
2011 $140,000 40% $42,000 (*1) $98,000
2012 $98,000 40% $39,200 (*2) $58,800
2013 $58,800 40% $23,520 (*3) $35,280
2014 $35,280 40% $14,112 (*4) $21,168
2015 $21,168 40% $1,168 (*5) $20,000
(*1) $140,000 x 40% x 9/12 = $42,000
(*2) $98,000 x 40% x 12/12 = $39,200
(*3) $58,800 x 40% x 12/12 = $23,520
(*4) $35,280 x 40% x 12/12 = $14,112
(*5) $21,168 x 40% x 12/12 = $8,467
--> Depreciation for 2015 is $1,168 to keep book value same as salvage value.
--> $21,168 - $20,000 = $1,168 (At this point, depreciation stops.)
[Example, 150% declining balance depreciation]
On April 1, 2011, Company A purchased an equipment at the cost of $140,000. This
equipment is estimated to have 5 year useful life. At the end of the 5th year, the salvage
(residual value) will be $20,000. Company A recognizes depreciation to the nearest whol
month. Calculate the depreciation expenses for 2011, 2012 and 2013 using double decli
balance depreciation method.
Useful life = 5 years --> Straight line depreciation rate = 1/5 = 20% per year
Depreciation rate for double declining balance method
= 20% x 150% = 20% x 1.5 = 30% per year
Depreciation for 2011
= $140,000 x 30% x 9/12 = $31,500
Depreciation for 2012
= ($140,000 - $31,500) x 30% x 12/12 = $32,550
Depreciation for 2013
= ($140,000 - $31,500 - $32,550) x 30% x 12/12 = $22,785
150% Declining Balance Depreciation Method
Book Value Depreciation Book Value at
Year Depreciation Rate
at the beginning Expense year-end
2011 $140,000 30% $31,500 (*1) $108,500
2012 $108,500 30% $32,550 (*2) $75,950
2013 $75.950 30% $22,785 (*3) $53,165
2014 $53,165 30% $15,950 (*4) $37,216
2015 $37,216 30% $11,165 (*5) $26,051
2016 $26,051 30% $6,051 (*6) $20,000
(*1) $140,000 x 30% x 9/12 = $31,500
(*2) $108,500 x 30% x 12/12 = $32,550
(*3) $75,950 x 30% x 12/12 = $22,785
(*4) $53,165 x 30% x 12/12 = $15,950
(*5) $37,216 x 30% x 12/12 = $11,165
(*6) $26,051 x 30% x 12/12 = $7,815
--> Depreciation for 2016 is $6,051 to keep book value same as salvage value.
--> $26,051 - $20,000 = $6,051 (At this point, depreciation stops.)
Sum-of-the-years'-digits method
Depreciation expense = (Cost - Salvage value) x Fraction
Fraction for the first year = n / (1+2+3+...+ n)
Fraction for the second year = (n-1) / (1+2+3+...+ n)
Fraction for the third year = (n-2) / (1+2+3+...+ n)
...
Fraction for the last year = 1 / (1+2+3+...+ n)
n represents the number of years for useful life.
[Example, Sum-of-the-years-digits method]
Company A purchased the following asset on January 1, 2011.
What is the amount of depreciation expense for the year ended December 31, 2011?
Acquisition cost of the asset --> $100,000
Useful life of the asset --> 5 years
Residual value (or salvage value) at the end of useful life --> $10,000
Depreciation method --> sum-of-the-years'-digits method
Calculation of depreciation expense
Sum of the years' digits = 1+2+3+4+5 = 15
Depreciation for 2011 = ($100,000 - $10,000) x 5/15 = $30,000
Depreciation for 2012 = ($100,000 - $10,000) x 4/15 = $24,000
Depreciation for 2013 = ($100,000 - $10,000) x 3/15 = $18,000
Depreciation for 2014 = ($100,000 - $10,000) x 2/15 = $12,000
Depreciation for 2015 = ($100,000 - $10,000) x 1/15 = $6,000
Sum of the years' digits for n years
= 1 + 2 + 3 + ...... + (n-1) + n = (n+1) x (n / 2)
Sum of the years' digits for 500 years
= 1 + 2 + 3 + ...... + 499 + 500
= (500 + 1) x (500 / 2) = (501 x 500) / 2 = 125,250
