# Sum of the digits

(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.