TM321 Lecture No.8

8/3/2019 TM321 Lecture No.8

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DEPRECIATION

Lecture No. 8


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Definition

Depreciation is decrease in valueof an asset due to:

Deterioration; Wear and tear;

Obsolescence; or

Depletion of resources.


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The purpose of determining theamount of depreciation

Accounting for legal and taxation reasons.

Ensuring that the cost of an asset isrecovered over its life.

For example, in operating equipment, sayas truck, a cost associated withdepreciation has to be recovered to

replace the equipment once it is retired.


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Estimation of Depreciation

It is difficult to estimate the exact rate andextent of depreciation of an asset as thisdepends on the extent of use; and resalemarket value.

In practice, depreciation are accountingentries into books.

Depreciation plans may take advantage of

taxation, as depreciation is considered as acost, may be used to off-set amount oftaxation (or delay tax payments).


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Calculating depreciation

Three main empirical methods:

Writing off fixed similar value every

year;Writing off a greater proportion in the

early years; and

Writing off a smaller proportion in theearly years.


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Depreciation Methods:

I: Straight line Depreciation Method

II: Declining Balance DepreciationMethod:

III: Sum-of-years-digits (SOYD)Depreciation

IV: Sinking Fund Method


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Straight line Depreciation Method:

Depreciates fixed similar value every year

Annual Straight line depreciation =

initial cost estimated salvage value

estimated life in years

if

P = Initial capital cost

L = asset salvage or resale value

N = estimated life of an asset in years


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Straight line Depreciation Method(Contd)

Then Book value, defined as currentproportion of the initial cost of an assetafter depreciation, is:

Book value =

LPkP /

Where k = number of years that the asset has been depreciated.


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Declining Balance DepreciationMethod:

Writes off at a greater rate in earlyyears.

Other names:Diminishing balance;

Matheson formula; or

Constant percentage


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Declining Balance DepreciationMethod (Contd..)

Fixed percentage of the book value written offannually;

Book value at year 0 = P

Book value at year 1 = P(1-d)1

Book value at year 2 = P(1-d)2

Book value at year k = P(1-d)k

Where d is the fixed percentage depreciatedat the end of asset life, book value is equal tosalvage value after n years.


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Declining Balance DepreciationMethod (Contd..)

Thus:

It follows from above that:

d is normally expressed as a percentage.

ndPL 1

nP

Ld 1


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Sum-of-years-digits (SOYD)Depreciation:

This method depreciates greater proportionin early years.

Example:

If an asset has 5 years estimated life, then

depreciation in the first to the fifth year will be

as follows:


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Sum-of-years-digits (SOYD)Depreciation (contd..)

1st Year:

2nd Year:

3rd Year:

5th Year:

P 54321

5

P 543214

LP153

LP15

1


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Depreciation for any one particular year, k:

Where: Dk = depreciation cost required;

P = initial capital cost;

L = salvage or resale value N = total life of asset

K = sequential year number

P

nn

knDk

2/1

1


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Book value is given by the formula:

nnknknLPBV

k

1

1


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Sinking Fund Method

Assumes a deposit of a uniformseries at a given rate of interest

The amount deposited accumulatesto the amount of depreciation at the

end of asset life.

S


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Sinking Fund Method(Contd..)

Example:

If initial cost is Tshs 10,000,000

Salvage is Tshs. 2,000,000 after 8 years

Interest is 10% p.a

Then end-of-year payments:

(10000-2000) (A/F, 10%,8) = 8000 (0.0874) = 699.20

Si ki F d M h d


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Total amount of accumulated imaginarypayments + interest at the end of k:

Is the loss of value after k years.

iAFniFALP ,/%,,/

Si ki F d M h d


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Thus, book value:

iAFniFALPPBVk

,/%,,/


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Graphical Comparisons:

Example:

An asset has cost Tshs. 10,000,000 and isestimated to last for 8 years when the

salvage value is expected to be Tshs.2,000,000.


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Graphical Comparisons (Contd..)

Compute and plot book values against ageof the asset using:

Straight-line method of depreciation;

Sum-of-years-digits method;

Declining balance method; and

Sinking fund method (at i = 10%)

Use the same axes.

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TM321 Lecture No.8