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 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

     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 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