# Depreciation

In depreciation, plant asset’s cost allocating over the period of assets. This process included the asset’s allocation, expenses against revenue over the asset’s life.
Depreciation methods
Straight line
Unit of production
Declining balance
Sum of year-digits

## Straight-line method

In the straight-line method, In each year of assets use, an equal amount of depreciation assigned. Depreciable cost is divided by useful life in years to the expense.
Straight-line depreciation per year=$\frac{Cost-Residual&space;value}{useful&space;life&space;in&space;years}$

=$\frac{41000-1000}{5}$
=8000

### A unit of production method

In the unit of production(UOP) method. In the plant assets, a fixed amount of depreciation charged. Depreciable cost is divided by useful life in units to determine this amount. This per-unit expense is multiplied by the number of units produced each period to compute for the period.n
Units-of-production per unit of output =$\frac{Cost-residual&space;value}{Usefullife&space;in&space;units}$

=$\frac{41000-1000}{400,000&space;miles}$
=\$.10

##### Double-Declining balance(DDB) method

– In Double-declining balance(DDB), a longer amount of asset’s cost of its useful life writes off than does straight-line, DDB  multiplying the asset’s book value, through a constant percentage, which is two times the straight-line depreciation rate.DDB amounts computed as follows.
First, the straight-line depreciation rate per year computed.
Second, the straight-line rate  multiplied by 2 to compute the DDB rate
Third, The DDB rate multiplied by the periods beginning asset book value cost less accumulated depreciation. The residual value of the asset ignored in computing depreciation by the DDB method except during the last year.
DDB rate per year=$(\frac{1}{useful&space;life&space;in&space;a&space;year}\times&space;2)=\frac{1}{5&space;years}\times&space;2$

=$(20%\times&space;2)=40%$
Fourth, the final year’s amount needed to reduce the assets’ book value.

4)

###### Sum-of-year-Digits(Syd) method

In the sum-of-years digits(Syd) method another accelerated method of depreciation  figured by multiplying the depreciable cost of the asset by a fraction is the sum of years’ digit for a 5-year asset the year’s digits are 1,2,3,4 and 5 and their sum is 15(1+2+3+4+5=15)
Sum of the years’digits=N(N+1)/2
Where N is the useful life of the asset expressed in years, for example, when N equals 5, we have $5\frac{(5+1)}{2}=\frac{30}{2}=15$
The numeration of the SYD fraction for the first year of a 5 year asset is 5, The numerator is 4 for the third year,2 for the fourth year, and 1 for the fifth year.
The SYD equation for the limit.
SYD depreciation per year       =$(Cost-Residual&space;value)\times&space;\frac{Years'digits,largest&space;first}{Sum&space;of&space;years'digits}$

=$(41000-1000)\times&space;\frac{^{5\bigstar&space;}}{1+2+3+4+5}$
=$40000\times&space;\frac{5}{15}=13,333$