### Depreciation

Straight line method depreciates cost evenly through out the useful life of the fixed asset. Straight line depreciation is calculated as follows:

$\mathrm{Depreciation \ per\ annum = \frac{(Cost - Residual\ Value)}{ Useful \ Life}}$

$D_{j} =\frac{C - S_{n}}{n}$

C= Cost of Purchase S$_n$ = Salvage value after n years n = no. of years

Sum of the years’ digits depreciation method, like reducing balance method, is a type of accelerated depreciation technique that allocates higher depreciation expense in the earlier years of an asset’s useful life.

Calculation of depreciation under this method can be summarized in the following 4 steps:

Step 1: Calculate the sum of the years’ digits in an asset’s useful life

For an asset having a useful life of 4 years, the sum of the years’ digits will be calculated as follows:

Sum of years’ digits = 4 + 3 + 2 + 1 = 10

Step 2: Calculate the depreciable amount

Depreciable amount, as with all depreciation methods, is equal to:

Asset’s cost of acquisition or construction including any subsequent capital expenditure
Less: Estimated residual value or scrap value at the end of the asset’s useful life

Step 3: Calculate the un-depreciated useful life

Un-depreciated useful life is equal to the number of years in the asset’s useful life that have not yet been subjected to depreciation.

Hence, for an asset that has a useful life of 4 years, the un-depreciated useful life to be used in calculating depreciation shall be 4 years in the first year of depreciation, 3 years in the second year and so on.

Step 4: Calculate depreciation using the sum of years’ digits & un-depreciated useful life

Reducing Balance Method charges depreciation at a higher rate in the earlier years of an asset. The amount of depreciation reduces as the life of the asset progresses. Depreciation under reducing balance method may be calculated as follows:

$\mathrm{Depreciation\ per\ annum}$ =
$\mathrm{(Net \ Book \ Value \ - Residual\ Value) x Rate \%}$

Where Net Book Value is the asset’s net value at the start of an accounting period. It is calculated by deducting the accumulated (total) depreciation from the cost of the fixed asset.
Residual Value is the estimated scrap value at the end of the useful life of the asset. As the residual value is expected to be recovered at the end of an asset’s useful life, there is no need to charge the portion of cost equaling the residual value.
Rate of depreciation is defined according to the estimated pattern of an asset’s use over its life term.

Depreciation using the sum of the years’ digits method can be calculated using the following formula:

Depreciation Expense = Un-depreciated useful life (Step 3) x Depreciable Amount (Step 2) Sum of the years’ digits (Step 1)

In ACRS system, D$_j$ = (Factor) * C and this factor is according to the table given in the table on page 115 of NCEES FE Reference Handbook.

Modified Accelerated Cost Recovery System (MACRS) depreciation always depreciates to zero; no salvage value considered, MACRS recovery time is always n+1 years. The MACRS is the current tax depreciation system in the United States.

### Solved Example:

#### 9906-01

Determine the present value of a building that was constructed 30 years ago at \\$50,000. The estimated life of the building is 50 years, at the end of which it will have 10% scrap value of its cost of construction. Depreciation is to be calculated by straight line method. (SSC JE CE Paper 9 Oct 2020 Morning)

### Solved Example:

#### 9906-02

The value at the end of the utility period without being dismantled is termed as: (UPPCL JE CE 2020)

### Solved Example:

#### 9906-03

The book value of a property in a particular year is the: (SSC JE CE Paper 9 Oct 2020 Morning)