Sinking fund (SF) depreciation method:-

In this method it is assumed that money is deposited in a sinking fund over the useful life that will enable to replace the asset at the end of its useful life. For this purpose, a fixed amount is set aside every year from the revenue generated and this fixed sum is considered to earn interest at an interest rate compounded annually over the useful life of the asset, so that the total amount accumulated at the end of useful life is equal to the total depreciation amount i.e. initial cost less salvage value of the asset. Thus the annual depreciation in any year has two components. The first component is the fixed sum that is deposited into the sinking fund and the second component is the interest earned on the amount accumulated in sinking fund till the beginning of that year.

For this purpose, first the uniform depreciation amount (i.e. fixed amount deposited in sinking fund) at the end of each year is calculated by multiplying the total depreciation amount (i.e. initial cost less salvage value) over the useful life by sinking fund factor. After that the interest earned on the accumulated amount is calculated. The calculations are shown below.

The first component of depreciation i.e. uniform depreciation amount ‘A' at the end of each year is given by;

(3.37)

Where i = interest rate per year

Depreciation amount for 1^st year is equal to only ‘A' as this is the amount (set aside every year from the revenue generated) to be deposited in sinking fund at the end of 1^st year and hence there is no interest accumulated on this amount.

Therefore

(3.38)

Now book value at the end of 1^st year is given by;

(3.39)

Depreciation amount for 2^nd year is equal to uniform amount ‘A' to be deposited at the end of 2^nd year plus the interest earned on the amount accumulated till beginning of 2^nd year i.e. on depreciation amount for 1^st year. Thus depreciation for amount for 2^nd year is given by;

Now putting ‘D₁' equal to ‘ A ' in the above expression results in;

(3.40)

Book value at the end of 2^nd year is given by;

Now putting the expressions of ‘BV₁' and ‘D₂' from equation (3.39) and equation (3.40) respectively in above expression results in the following;

(3.41)

Depreciation amount for 3^rd year is equal to uniform amount ‘A' to be deposited at the end of 3^rd year plus the interest earned on the amount accumulated till beginning of 3^rd year i.e. on sum of depreciation amounts for 1^st year and 2^nd year. Thus depreciation for amount for 3^rd year is given by;