Depreciation methods based on time
Straight line method
Declining balance method
Sum-of-the-years'-digits method
Straight Line Depreciation Method
[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 value (residual value) will be $20,000. Company A recognizes depreciation to the nearest whole 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
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 value (residual value) will be $20,000. Company A recognizes depreciation to the nearest whole month. Calculate the depreciation expenses for 2011, 2012 and 2013 using double declining 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
year book Value
at the beginning depreciation rate depreciation expense book Value at the year-end2011$140,00040%$42,000 (*1)$98,0002012$98,00040%$39,200 (*2)$58,8002013$58,80040%$23,520 (*3)$35,2802014$35,28040%$14,112 (*4)$21,1682015$21,16840%$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 value (residual value) will be $20,000. Company A recognizes depreciation to the nearest whole month. Calculate the depreciation expenses for 2011, 2012 and 2013 using double declining 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
Year Book Value
at the beginning Depreciation Rate Depreciation Experience Book Value at the year-end2011$140,00030%$31,500 (*1)$108,5002012$108,50030%$32,550 (*2)$75,9502013$75.95030%$22,785 (*3)$53,1652014$53,16530%$15,950 (*4)$37,2162015$37,21630%$11,165 (*5)$26,0512016$26,05130%$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.)
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
