Depreciation Value Formula

Depreciation is the reduction in the value of the asset year by year due to wear and tear. Depreciation can be calculated using the straight line depreciation method or the accelerated depreciation method.

The straight line method calculates the depreciation  by spreading the cost evenly over the life period of the fixed asset.
Accelerated depreciation method calculates the depreciation by expensing  a large part of the cost at the beginning of the life of the fixed asset.



Formula for Straight line depreciation method =  Cost / life.

Ex :- The cost of a machine is $ 100.  It is expected to last for 4 years. Calculate the annual depreciation.

Sol:  Cost of the machine = $ 100

Expected time         =       4

Therefore annual depreciation is 100 / 4 = $25

Every year $25 would be expensed as depreciation value.

In this method the salvage value is not taken into account.
Depreciation Value:

Another method used is called accelerated depreciation  method  or declining balance depreciation method. It uses a factor based on the life of the asset. The factor is the percentage of the asset that would be depreciated each year under straight line depreciation times the accelerator.

Let us take the cost of the machine that is $100. Under this system we double the depreciation period a 50% from 25%. This is called double declining balance

Ex:  Cost of a machine is $100.  Its life period is 4 years.  What is the depreciation factor?

Sol: The depreciation factor is calculated  by doubling  as 200% = 2 * (1/4) = 0.50

So the calculation runs like this:-

Year              Depreciable basis   Depreciation calculation    Depreciation expenses  Accumulated depreciation

1                     $100                       100 * 0.5                              50                                  50

2                     $  50                        50 * 0.5                              25                                   75

3                     $  25                        25 * 0.5                              12.50                              87.50

4                     $  12.50                 12.5 * 0.5                                6.25                              93.75

So over the  four years the depreciation has been $ 93.75

The salvage value is $100 - $93.75 = $6.25

This depreciation value formula is adopted by most of the manufacturing units where there is considerable wear and tear.

It is also used by  transport system such as lorries, goods carrier where the wear and tear is considerable.
Formula of Depreciation Value :

There is yet another formula for finding the depreciation value. It is  written as  A= P( 1 - i)n

A = the depreciated amount : P = the present value ;  i = rate of depreciation and n = number of years.

It is also written as FV = PV ( 1 - i)n  where FV is future value ; PV = present value ; i = rate of depreciation and n = number of years.

We use the subtraction sign (1 - i) because the value goes down.

Let us do a problem using this formula.

Ex: A machine depreciates  in value each year at the rate of 10% of its value at the beginning of a year.  The machine was purchased for $10,000.  Obtain its value at the end of 10th year.

Sol:

Present value = PV = $10,000

rate of depreciation =10% = 0.1

Number of years = 10                                                                                                                          _                               _

So   FV = 10,000 ( 1 -0.1)10  = 10,000 (0.9)10  = log  0f 10,000 + 10 log 0.9 = 4.0000 + 10 x  1.9542 = 4.0000 + 1.5420

=  3.5420

Antilog of  3.5420 = 3483

Hence the depreciated value of the machine whose purchase price was $10,000  at the depreciation rate of 10% for 10 years becomes $ 3,483

Ans = $ 3,483