During 2016 and 2017, Faulkner Manufacturing used the sum-of-the-years’-digits (SYD) method of depreciation for its depreciable assets, for both financial reporting and tax purposes. At the beginning of 2018, Faulkner decided to change to the straight-line method for both financial reporting and tax purposes. A tax rate of 40% is in effect for all years. For an asset that cost $21,000 with an estimated residual value of $1,000 and an estimated useful life of 10 years, the depreciation under different methods is as follows:

The value to depreciate is the total asset cost minus the salvage or residual value. In this case, $21,000-$1000=$20,000. The straight line method formula is:

Depreciation = value to depreciate/useful years

Depreciation (each year) = $20,000/10= $2,000

Each year the depreciation expense is $2,000

The sum of the years-digits method formula is:

depreciation (year 1) = value to depreciate*depreciation coefficient (year 1)

depreciation (year 2) = value to depreciate*depreciation coefficient (year 2)

and so on until year 10.

To calculate the depreciation coefficient you must use this formula:

depreciation coefficient= decreasing year/ digits sum

The digits sum is the sum of all the useful life years, in this case is:

Digits sum= 1+2+3+4+5+6+7+8+9+10= 55

Depreciation coefficient( year 1): 10/55= 0.1818*100=18.2%

Depreciation coefficient( year 2): 9/55= 0.1636*100=16.4%

Depreciation coefficient( year 3): 8/55= 0.1454*100=14.5%

And so on until year 10:

Depreciation coefficient (year 10): 1/55= 0.0181*100= 1.8%

Then, the depreciation expense for the first year is:

Depreciation (year1)= $20,000*18.2%= $3,636

Depreciation (year2)= $20,000*16.4%= $3,273

The table attached shows the depreciation expense for 10 year using both methods.

At the end, the sum of all depreciation expenses must be the value to depreciate that in this case is $20,000.