WEBVTT
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Welcome to the course depreciation alternate
investment and profitability analysis we are
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continuing with module one that is depreciation
The topic of today’s lecture is declining-balance
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method this is a depreciation method When
the declining-balance method is used the annual
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depreciation cost is a fixed percentage of
the property value at the beginning of the
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particular year
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The fixed percentage or declining-balance
factor remains constant through the entire
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service life of the property while the annual
depreciation is different in each year The
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depreciation per annum is equal to net book
value into a constant percentage which is
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given here by rate percent
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Under these conditions the depreciation cost
for the first year of the property life is
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V into f where f represents the fixed percentage
factor So we can write down the depreciation
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for first year is V into f and the book value
at the end of the first year or we can say
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the start of the second year is equal to book
value is equal to V minus V into f If we take
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V common this is V in the brackets 1 minus
f Book Value at the end of the first year
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is V1 if we consider it to be V1 this is equal
to V into 1 minus f at the end of the second
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year if I consider it to be V2 then it is
V into 1 minus f whole square and at the end
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of the ‘a’ th year this is Va is equal
to V into 1 minus f to the power a
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Now at the end of the N th year this is obviously
at the end of the N th year the value becomes
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Vs that is salvage value and we can write
down Vs is equal to V into 1 minus f to the
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power N So we can write down here Vs is equal
to V into 1 minus f to the power N now if
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this f the fix factor is unknown So from this
equation we can find out this fix factor and
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this fix factor is f 1 minus f to the power
N is equal to Vs by V or 1 minus f is equal
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to Vs by V to the power 1 by N or f is equal
to 1 minus Vs by V to the power 1 minus N
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Now this is the equation to find out the value
of the fixed factor f Now we will see that
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the depreciation rate is not constant in this
declining-balance as shown in the left hand
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side figure the depreciation is more during
the
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in the straight line this is something like
this and the declining-balance this is something
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like this this is declining-balance This equation
which is equation number one represents the
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textbook method for determination of the fixed
percentage factor and the equation is sometimes
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designated as the Matheson formula Comparison
with the straight line method shows that declining-balance
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depreciation permits the investment to be
paid of more rapidly during the early years
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of the life
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Declining balance method is appropriate where
an asset has a higher usage in the early years
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of its life For instance computers and its
accessories have better usage in the early
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years these also becomes absolute in a span
of few years due to advent of new technologies
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Use of declining-balance method to depreciate
computer equipment would ensure higher depreciation
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in the early years of its operation
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The increased depreciation cost in the early
years are very attractive to concerns just
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in starting phase of business why At the starting
phase of business the company has put a lot
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of money into the business and it is always
short of money but during that period at the
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starting phase if it pays more tax or returns
the money more money in terms of tax then
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it will overload the business Because the
income tax load reduced at the time when it
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is most necessary to keep all pay out cost
at a minimum and this is why if the depreciation
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cost in the early ages are more than one have
to pay less income tax in early ages and for
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this purpose declining-balance method is good
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To apply declining-balance method it should
be noted that the value of the asset cannot
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decrease to zero at the end of the service
life and may possibly be greater than the
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salvage value or the scrap value Let me explain
this if I am using declining-balance method
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this is my Vs point it may reduce to a value
which is greater than previous and hence what
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is being done after some period of time one
switches to straight line method of depreciation
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to bring the salvage value to its original
value
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To handle this difficulty it is sometimes
desirable to switch from the declining-balance
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to a straight line method as I have done this
here I have switched declining-balance method
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to straight line method here switch from the
declining-balance to the straight-line method
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after a portion of the service has expired
This is known as the combination method as
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shown in the figure in the right hand side
it permits the property to be fully depreciated
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during the service life yet also gives the
advantage of faster early-life write-offs
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So the both properties are combined when I
am using a combination method that means the
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first recovery in the early period and then
reaching to the Vs in the later period when
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I am using a straight-line method The figure
in the right hand side also shows the effect
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of time on asset value when the declining-balance
method of depreciation is used with an arbitrarily
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chosen value of f
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Now start with the examples and take the first
example the first example is the original
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value of a piece of equipment is rupees 33000
completely installed and ready to use its
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salvage value is RS 3000 at the end of a service
life estimated to be 10 years Determine the
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asset or book value of the equipment at the
end of 5th year using declining-balance method
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Now what is given given V it is equal to 33000
at the initial value of the asset Vs is equal
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to 3000 N is equal to 10 and we need to calculate
what is V5 The asset value or the book value
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at the end of 5th year Now the fixed percentage
factor
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is equal to 1 minus Vs minus V to the power
1 by N Now here Vs is the salvage value V
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is the original value and this factor f is
equal to 1 minus 3000 by 33000 to the power
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1 by 10 So we can calculate this
this is equal to 1 minus 3000 divided by 33000
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comes out to be 0.09091 to the power 0.1 This
is equal to 1 minus 0.786794 and this equal
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to 0.2132 that is 21.32 percent
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Now we have computed the f factor this comes
out to be 21.32 or 21.32 percent Now we can
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calculate book value
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Book value at the end of 5th year is equal
to V5 is equal to V into 1 minus f to the
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power 5 This is 33000 into 1 minus 0.2132
to the power 5 and this comes about comes
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to be rupees 9950.289 this is our answer
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The second example is the original value of
a piece of equipment is 33000 completely installed
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and ready for use Its salvage value is rupees
3000 at the end of a service life If the fixed
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percentage factor for depreciation is 21.33
percent determine the service life of the
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equipment Now we do not know the value of
N where the value of f is given 0.2133 So
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my V is given the original value of the equipment
Vs is given 3000 f is given 0.2133 but N is
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not given I have to calculate the value of
N
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Now we start with our formula first percentage
factor is equal to 1 minus Vs by V to the
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power 1 by N or Vs by V to the power 1 by
N is equal to 1 minus f and this is equal
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to 1 minus 0.2133 which is equal to 0.7867
Now if we calculate Vs by V this is 33000
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divided by sorry this is 3000 by 33000 and
which comes out to be 0.090909 So 0.090909
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to the power 1 by N is equal to 0.7867
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Now if I take log N is equal to log Vs by
V divided by log 0.7867 this is equal to Ln
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0.090909 divided by Ln 0.7867 and this is
equal to 9.995 or I can say 10 years So this
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is the answer of the example number two So
N is 10 years Let us move to example number
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three again the same numerical is used but
with a twist
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The original value of a piece of equipment
is rupees 33000 completely installed and ready
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for use The service life of the equipment
is 10 years if the fixed percentage factor
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for depreciation is 21.32 percent determine
the salvage value of the equipment Basically
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here I would like to explain our basically
equation is f is equal to 1 minus Vs by V
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to the power N This is the equation every
time I am using to calculate different values
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Here if we see in this equation the variables
are f Vs V and N So there are 4 variables
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and this is a single equation and the single
equation can only give the value of a single
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unknown that means if I supply the values
of these three I can calculate out N or if
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I supply the value of these three I can calculate
this one or if I supply value of these three
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I can calculate this or if I supply
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of this then I can calculate this one
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So this is how the questions are framed In
this case we have to find out what is value
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of Vs So f is given V is given and N is given
So this is example number three
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given V is given 33000 Vs is unknown f is
equal to 0.2132 N is equal to 10 So we have
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0.2132 is equal to 1 minus Vs by V to the
power one by N Now Vs by V is equal to 3000
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divided by 33000 Here we do not know the value
of Vs basically this is unknown this is unknown
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So I can write down Vs by V is equal to 1
minus f to the power N is equal to 1 minus
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0.2132 to the power 10 this comes out to be
this is 0.7868 to the power 10 to the power
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10 comes out to be 0.09091 So Vs is equal
to 33000 into 0.09091 is equal to rupees into
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33000 comes to be 3000 25paisa So my answer
is Vs is equal to
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Now let me summarize today’s lecture The
monetary value of an asset decreases over
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time due to use wear and tear or obsolescence
This decrease measured as depreciation and
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can be used as a means of distributing the
original cost of a physical asset over the
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life period during which the asset is in use
employing many methods The present lecture
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demonstrates how to use declining-balance
method for depreciation computations and also
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shows where you should use declining-balance
method and what benefits you can extract using
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declining-balance method in taxation Thank
you