Depreciation

Depreciation is the process of allocating the cost of 
long-lived assets over the useful life of the asset
  
Depreciation base  = cost of the asset - residual value
Amount to be depreciated each period is determined by 
the depreciation method applied
    

Residual value

The value expected to remain when the asset is retired 
at the end of useful life
  

Depreciation base

The total amount to be depreciated 
over the life of the asset
Depreciation base = cost of the asset - residual value  
 
An example
Entity A purchased an equipment at the cost of $800,000
Useful life of the equipment = 10 years
Estimated residual value = $50,000
What is the amount of depreciation base?

  
Depreciation base = $800,000 - $50,000 = $750,000
  

Depreciation methods

To allocate the deprecation base to each period over the life of the asset, depreciation methods are applied
Depreciation methods should be systematic and rational
Depreciation can be based on the time elapsed or 
the specific usage of the asset
  
Depreciation methods based on the time elapsed
1. Straight line deprecation method
2. Declining balance deprecation method
3. Sum-of-the-years'-digits depreciation method
  
Depreciation methods based on the specific usage 
of the asset
1. Based on the units of production
2. Based on the operation hours of the asset
  

Straight line depreciation method

Under the straight line method, 
depreciation amount for each period is 
same for all periods
Depreciation = (cost - residual value) / use life
  
An example
Entity A purchased an equipment at the cost of $650,000
Useful life = 10 years
Residual value = $50,000
Entity A uses the straight line depreciation method for equipment

What is the amount of annual depreciation of 
this equipment?
What is the amount of monthly depreciation of 
this equipment?
    
Annual depreciation  = (cost - residual value) / useful life
   = ($650,000 - $50,000) / 10 
   = $600,000 / 10 = $60,000  
     
Monthly depreciation  = annual depreciation / 12
   = $60,000 / 12 = $5,000 
  

Declining balance depreciation method

Under the declining balance method, 
depreciation is calculated by multiplying a depreciation rate to 
the beginning book value of the asset
  
Depreciation = beginning book value x depreciation rate
Book value = cost - accumulated depreciation
Depreciation rate is determined as a percentage of the straight line method depreciation amount

Examples of depreciation rates under straight line method
Useful life of the asset = 10 years
Yearly depreciation rate = 1/10 = 10%

Useful life of the asset = 20 years
Yearly depreciation rate = 1/20 = 5%
  
Declining balance deprecation methods
1. Double declining balance method
     Depreciation rate = straight line depreciation rate x 200%
  
2. 150% declining balance method
      Depreciation  rate = straight line depreciation rate x 150%
  

Double declining balance depreciation method

Under the double declining balance method
     Depreciation rate = straight line depreciation rate x 200%
     Depreciation = beginning book value x depreciation rate
 
An example
On January 1, 20X1, Entity A purchased an equipment at the cost of $500,000
Residual value = $40,000
Useful life = 10 years
Entity A applies double declining balance method to depreciate equipment
What is the amount of deprecation for the year ended December 31, 20X1?
     
Straight line depreciation rate = 1/10 = 10% per year
Double declining balance depreciation rate
   = straight line depreciation rate x 200%
   = 10% x 2 = 20% per year
 
Depreciation = beginning book value x depreciation rate
Beginning book value = cost - accumulated depreciation
   = $500,000 - 0 = $500,000
Depreciation = $500,000 x 20% per year = $100,000
  

150% declining balance depreciation method

Under the 150% declining balance method
     Depreciation rate = straight line depreciation rate x 150%
     Depreciation = beginning book value x depreciation rate
 
An example
On January 1, 20X1, 
Entity A purchased an equipment at the cost of $500,000
Residual value = $40,000
Useful life = 10 years
Entity A applies 150% declining balance method to depreciate equipment
What is the amount of deprecation for the year ended December 31, 20X1?
     
Straight line depreciation rate = 1/10 = 10% per year
150% declining balance depreciation rate
   = straight line depreciation rate x 150%
   = 10% x 1.5 = 15% per year
 
Depreciation = beginning book value x depreciation rate
Beginning book value = cost - accumulated depreciation
   = $500,000 - 0 = $500,000
Depreciation = $500,000 x 15% per year = $75,000
  

Sum-of-the-
years'-digits depreciation method

Under the sum-of-the-years'-digits method,
   depreciation = (cost - residual value) x depreciation factor

An example
Entity A purchased an equipment at the cost of $500,000
Residual value = $50,000
Useful life = 5 years
  
Sum-of-the-years'-digits = 1 + 2 + 3 + 4 + 5 = 15
  
Depreciation factor for year 1 = 5 / 15
Depreciation factor for year 2 = 4 / 15
Depreciation factor for year 3 = 3 / 15
Depreciation factor for year 4 = 2 / 15
Depreciation factor for year 5 = 1 / 15
  
Depreciation for year 1 = ($500,000 - $50,000) x (5/15)
   = $450,000 x 5/15 = $150,000
Depreciation for year 2 = ($500,000 - $50,000) x (4/15)
   = $450,000 x 4/15 = $120,000
Depreciation for year 3 = ($500,000 - $50,000) x (3/15)
   = $450,000 x 3/15 = $90,000
Depreciation for year 4 = ($500,000 - $50,000) x (2/15)
   = $450,000 x 2/15 = $60,000
Depreciation for year 5 = ($500,000 - $50,000) x (1/15)
   = $450,000 x 1/15 = $30,000
  

Units of production based depreciation method

Depreciation = (cost - residual value) x depreciation factor
Depreciation factor = (A) / (B)
   (A) = Number of units produced during the year using the asset
   (B) = Total number of units expected to be produced during the life of the asset
  
An example
Entity A purchased an asset at the cost of $270,000
Residual value = $20,000
Useful life = 5 years
  
(A) = Number of units produced during the year using the asset 
= 25,000 units

(B) = Total number of units expected to be produced 
during the life of the asset = 125,000 units
        
Depreciation for the year = ($270,000 - $20,000) x (25,000/125,000)
   = $250,000 x 1/5 = $50,000
  

Hours of operation based depreciation method

Depreciation = (cost - residual value) x depreciation factor
Depreciation factor = (C) / (D)
   (C) = Number of hours the asset was in operation during the year
   (D) = Total number of operation hours expected 
during the life of the asset = 18,000 hours   
An example
Entity A purchased an asset at the cost of $390,000
Residual value = $30,000
Useful life = 5 years
  
(C) = Number of hours the asset was in operation during the year 
= 3,000 hours

(D) = Total number of operation hours expected 
during the life of the asset = 18,000 hours
        
Depreciation for the year = ($390,000 - $30,000) x (3,000/18,000)
   = $360,000 x 1/6 = $60,000