Depreciation and its methods

Depreciation

It is the decrease in the worth of physical properties with the passage of time and use. It is a non cash outlay that declines the value of an asset as a result of wear and tear or age and obsolescence. Most assets depreciate over period and must be changed once the end of their useful life is reached. It is an accounting concept that creates a yearly deduction against tax income such that the effect of time and use on asset’s value can be revealed in a firm’s financial reports.

An asset can only be depreciated if they meet the following basic requirements:

1. Must be an asset which decays, gets used up, wears out, becomes obsolete, or loses value to the owner from natural causes.
2. Must have useful life that can be known and their life must be longer than one year
3. Must be used for business purpose to produce income

Depreciable property can be tangible as well as intangible. Tangible property can be perceived or touched and includes private property such as machinery, vehicles, equipment, furniture, etc. and real property as land. Intangible property comprises copyright, patent, goodwill, trademark, etc.

Depreciation occurs due to:

1. Use related physical loss
2. Time related physical loss
3. Functionally related loss
4. Sudden Failure
5. Depletion

Some Terminologies:

1. Cost basis:

Initial cost of the assets including purchase price, delivery and installation fees and other depreciable costs incurred to set up the asset for use.

2. Book value:

Represents the remaining undepreciated principal investment on the book value after the total amount of depreciation charges to date have been deducted from the basis. The book value is usually determined at the end of each year.

3. Recovery period:

It is the depreciable life ‘n’ of the assets in years.

4. Salvage value ‘S’:

It is the estimated value of the property at the end of its useful tenure. It is the estimated selling price of a goods when the asset can no longer be used productively by its owner.

5. Useful life:

It is the estimated period of time that a property will be used in a trade of business or to produce income.

6. Market value (MV):

It is defined as the amount that will be paid by the willing purchaser to a willing seller for a property where they have equal benefit and is under no compulsion to buy or sell. The Market Value approximates the present value of what will be developed through ownership of the property, including the time value of money.

Methods of Depreciation:

1. Straight Line Method

This is the simplest and most common used depreciation method. It assumes that a same amount is depreciated every year over the useful life of the asset.

In this method, a fixed or equal amount is imposed as the depreciation amount over the lifetime of the asset such that the accumulated sum at the end of the useful life of the asset is exactly equal to the purchase value of the cost, i.e. the value of the assets will become zero.

D_n = (I – S)/N

Where, D_n = depreciation charge during year ‘n’

I = Cost of the assets including installation outlays

S = salvage value at the end of life

N = useful life

Book value in a given year = Cost Basis – Total depreciation charges to date

2. Declining/ Diminishing balance method:

Declining balance is also known as the fixed or uniform percentage method in which book value is multiplied by the fixed rate, α.

α= 1/N multiplier

The most frequently used multipliers is double the straight line rate, for this reason it is called Double Declining Balance Method.

Let a business has an asset with Rs.1,000 inventive cost, Rs.100 Salvage value and 5 years useful life. First, compute straight line depreciation rate. Since the asset has 5 years useful life then depreciation rate equals (100% / 5 =) 20% each year.

With double declining balance method, as the name recommends, double that rate or 40% depreciation is used.

We can determine depreciation charges for a given year, D_n as follows:

D₁ = αI

D₂ = α(I – D₁) = αI(1 – α)

D₃ = α(I – D₁ – D₂) = αI(1 – α)²

Thus for any year ‘n’, we have depreciation charge

D_n = αI(1 – α)^{n – 1} ………(i)

Total Declining Balance (TDB) at the end of year ‘n’ can be calculated as:

TDB = D₁ + D₂ + D₃ + …+ D_n

= αI + αI(1 – α) + αI(1 – α)² + …+ αI(1 – α)^{n – 1}

= αI{1 + (1 – α) + (1 – α)² + …+ (1 – α)^{n – 1}}………(ii)

Multiplying by (1 – α) on both sides, we obtain

(1 – α)TDB = αI{(1 – α) + (1 – α)² + (1 – α)³ + …+ (1 – α)ⁿ}………(iii)

Subtracting equation (ii) from (iii),

TDB = I{1 – (1 – α )ⁿ}

The book value ‘B’ at the end of each year will be

B_n = I – TDB = I - I{1 – (1 – α )ⁿ} = I(1 – α )ⁿ

Salvage value (S) must be projected at the beginning of depreciation analysis. It is unusual occurrence in the real world that the final book value (B_n) equals to the estimated salvage value. So when B_n ≠ S, we have to make the adjustments in our depreciation analysis technique. Here two cases arise:

Case 1: When B_N > S

This is the situation in which we have not depreciated the total cost of the asset. To decrease the book value of an asset to its salvage value, it can be done by switching to Straight Line (SL) from declining balance (DB). The switch from DB to SL depreciation can take place in any of the ‘n’ years (i.e. optimal year).

The switching rule is:

If depreciation by DB in any year is less than (or equal to ) the depreciation by SL, we would switch to and remain with SL method for the duration of the project’s depreciable lifetime.

The straight line depreciation in any year ‘n’ is calculated by

D_n = [Book value at the beginning of year n – Salvage value]/Remaining useful life

Case 2: When B_N < S

This is the situation in which book value is sluggish than Salvage value (S). We must readjust our study such that B_N = S because tax law does not permit us to depreciate the asset less than their salvage value.

3. Sum of Year’s Digit (SOYD method:

This method results in larger than straight line depreciation charges at the early years of an asset and smaller charges as the asset nears the end of its useful life. Each year depreciation charge is compounded as the remaining useful life at the beginning of the year divided by the sum of the years’ digit for the total valuable life.

In this method, the number 1, 2, 3, …N are summed, where N is the estimated years of valuable life.

SOYD = 1 + 2 + 3 + … + N = N.(N + 1)/ 2

The depreciation each year is calculated as

D_n = [(N – n + 1)(I – S)]/ SOYD

4. Sinking Fund Method:

In this method of depreciation, ^{the book value decreases at increasing rates with respect to the life of the asset.} The loss in value of asset (cost – Salvage) is made available and the form of cumulative depreciation amount at the end of the asset by setting up an equal depreciation amount at the end of the each period during the life time. This fixed amount depreciated at the end of every time period earns an interest at the rate of i% compounded annually.

Let,

P = initial cost of the asset

F = final salvage value

N = life of the asset

i = rate of return compounded annually (rate of interest)

A = the annual equivalent amount of depreciation charge

BV_k = the book value of the asset at the end of period k

D_t = the depreciation charge at the end of period t

To find the annual equivalent amount (A) = (P – F) × (A/F, i%, N)

To find the depreciation charge (D_t) = (P – F) × (A/F, i%, N) × (F/P, i%, t – 1)

To find the book value at the end of period t = P – (P – F) × (A/F, i%, N) × (F/P, i%, t)

BIBLIOGRAPHY:

Chan S.Park, Contemporary Engineering Economics, Prentice Hall, Inc.
E. Paul De Garmo, William G.Sullivan and James A. Bonta delli, Engineering
Economy, MC Milan Publishing Company.
James L. Riggs, David D. Bedworth and Sabah U. Randhawa,Engineering
Economics, Tata MCGraw Hill Education Private Limited.