Accounting Study Guide

    Depreciation methods based on time
           Straight line method
           Declining balance method          
           Sum-of-the-years'-digits method

    Depreciation based on use (activity)

    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

    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-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 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 Expense	Book Value at the 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.)

    
    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.