Sum of the digits: Difference between revisions

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(SOD).
(SOD).
1.
1.
A basis of allocating total costs or income across successive time periods, so as to 'front-end load' them.
A basis of allocating total costs or income across successive time periods, so as to 'front-end load' them.
In other words, a systematically greater proportion of the total cost or income is allocated to the earlier periods.
In other words, a systematically greater proportion of the total cost or income is allocated to the earlier periods.


For example, a fixed asset has a cost of $12m, an expected disposal value of $2m and an expected useful life of 4 years.
The total expected accounting cost for the 4 year period = $12m - $2m = $10m.


The 'sum of the digits' of the expected holding Years 1 to 4 inclusive = 1 + 2 + 3 + 4 = 10.
'''Example'''
 
A fixed asset has a cost of $12m,
 
an expected disposal value of $2m,
 
and an expected useful life of 4 years.
 
 
The total expected accounting cost for the 4 year period:
 
= $12m - $2m
 
= $10m.
 
 
The 'sum of the digits' of the expected holding Years 1 to 4 inclusive  
 
= 1 + 2 + 3 + 4  
 
= 10.
 


The allocation proportions (for the total depreciation charges of $10m) are calculated as follows:
The allocation proportions (for the total depreciation charges of $10m) are calculated as follows:


Year 1: 4/10 (x $10m = $4m).
Year 1:  
Year 2: 3/10 (x $10m = $3m).
 
Year 3: 2/10 (x $10m = $2m).
= $10m x 4 / 10
Year 4: 1/10 (x $10m = $1m).
 
= $4m.
 
 
Year 2:  
 
= $10m x 3 / 10  
 
= $3m.
 
 
Year 3:  
 
= $10m x 2 / 10  
 
= $2m.
 
 
Year 4:
 
= $10m x 1 / 10  
 
= $1m.
 


The net book value of the fixed asset - applying the depreciation charges calculated above - would be (at the end of each year):
The net book value of the fixed asset - applying the depreciation charges calculated above - would be (at the end of each year):
Year 1 = 12 - 4 = $8m.
 
Year 2 = 8 - 3 = $5m.
Year 1:
Year 3 = 5 - 2 = $3m.
 
Year 4 = 3 - 1 = $2m.
= 12 - 4  
 
= $8m.
 
 
Year 2:
 
= 8 - 3  
 
= $5m.
 
 
Year 3:
 
= 5 - 2  
 
= $3m.
 
 
Year 4:
 
= 3 - 1  
 
= $2m.
 
 


2.
2.
Sum of the digits methods are sometimes used to allocate total finance charges - for example under IAS 17 - as a simpler alternative to the Implied rate of interest (or Actuarial) method.
 
Sum of the digits methods are sometimes used to allocate total finance charges - for example under IFRS 16 - as a simpler alternative to the Implied rate of interest (or Actuarial) method.
 


== See also ==
== See also ==
* [[Actuarial method]]
* [[Actuarial method]]
* [[Depreciation]]
* [[Depreciation]]
* [[IAS 17]]
* [[IFRS 16]]
* [[Implied rate of interest]]
* [[Implied rate of interest]]
* [[Interest]]
* [[Reducing balance]]
* [[Reducing balance]]
* [[Straight line]]
* [[Straight line]]


[[Category:Accounting,_tax_and_regulation]]
[[Category:The_business_context]]
[[Category:Corporate_finance]]
[[Category:Investment]]
[[Category:Long_term_funding]]
[[Category:Financial_products_and_markets]]
[[Category:Trade_finance]]

Latest revision as of 08:29, 3 February 2022

(SOD).

1.

A basis of allocating total costs or income across successive time periods, so as to 'front-end load' them.

In other words, a systematically greater proportion of the total cost or income is allocated to the earlier periods.


Example

A fixed asset has a cost of $12m,

an expected disposal value of $2m,

and an expected useful life of 4 years.


The total expected accounting cost for the 4 year period:

= $12m - $2m

= $10m.


The 'sum of the digits' of the expected holding Years 1 to 4 inclusive

= 1 + 2 + 3 + 4

= 10.


The allocation proportions (for the total depreciation charges of $10m) are calculated as follows:

Year 1:

= $10m x 4 / 10

= $4m.


Year 2:

= $10m x 3 / 10

= $3m.


Year 3:

= $10m x 2 / 10

= $2m.


Year 4:

= $10m x 1 / 10

= $1m.


The net book value of the fixed asset - applying the depreciation charges calculated above - would be (at the end of each year):

Year 1:

= 12 - 4

= $8m.


Year 2:

= 8 - 3

= $5m.


Year 3:

= 5 - 2

= $3m.


Year 4:

= 3 - 1

= $2m.


2.

Sum of the digits methods are sometimes used to allocate total finance charges - for example under IFRS 16 - as a simpler alternative to the Implied rate of interest (or Actuarial) method.


See also