Sum-of-years-digits (SOYD) depreciation method:-

It is also an accelerated depreciation method. In this method the annual depreciation rate for any year is calculated by dividing the number of years left (from the beginning of that year for which the depreciation is calculated) in the useful life of the asset by the sum of years over the useful life.

The depreciation rate ‘d_m' for any year ‘m' is given by;

(3.21)

Where n = useful life of the asset as stated earlier

SOY = sum of years' digits over the useful life =

Rewriting equation (3.21);

(3.22)

The depreciation amount in any year is calculated by multiplying the depreciation rate for that year with the total depreciation amount (i.e. difference between initial cost ‘P' and salvage value ‘SV ') over the useful life.

Thus the expression for depreciation amount in any year ‘m ' is represented by;

(3.23)

Putting the value of ‘d_m' from equation (3.21) in equation (3.23) results in the following;

(3.24)

The depreciation in 1^st year i.e. ‘D₁' is obtained by putting ‘m ' equal to ‘1' in equation (3.24) and is given by;

(3.25)

The book value at the end of 1^st year is equal to initial cost less the depreciation in the 1^st year and is given by;

Now putting the expression of ‘D₁' from equation (3.25) in the above expression results in following;

(3.26)

The depreciation in 2^nd year i.e. ‘D₂' is given by;

(3.27)

Book value at the end of 2^nd year is equal to book value at the beginning of 2^nd year (i.e. book value at the end of 1^st year) less the depreciation in 2^nd year and is given by;