WEBVTT
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Welcome to the course Depreciation Alternate
Investment and Profitability Analysis We are
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continuing with module two which is alternative
investment In this lecture I will be covering
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perpetuity method which is a method to select
alternate investments Perpetuity or capitalized
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cost method because of the varying service
life it was necessary to arrive at a least
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common multiple of service lives in the present
worth method
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Sometimes it may be difficult and time-consuming
to arrive at a least common multiple of estimated
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lives of all the assets involved in study
In such cases it is much easier to compare
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the alternatives using capitalized cost method
Capitalized worth is the present worth of
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a perpetuity it indicates that the amount
of money needed at present time such that
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the interest earned will cover the cash flow
requirements forever for the investment This
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method is generally used by governments and
assumption is made here that the assets when
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renewed repeat their cost history
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Capitalized costs are annual costs divided
by the interest rate for example if rupees
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20000 at the end of 10 years at 10% interest
is required one has to pay 1254.91 a year
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and this value has been calculated from the
annuity formula which converts a future value
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to a annuity which has been given in the slide
For the ten preceding years for this case
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the capitalized cost becomes 1254.91 divided
by 0.1 which is the value of i which comes
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out to be 12549.1 which means that if 12549.1
is invested today that is now will become
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32549.1 in 10 years and if 20000 from this
is spent at the end of the 10 year then rupees
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12459.1 will remain and will again grow to
rupees 32549 after 10 years later
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Thus the cycle of payment of rupees 20000
at the end of 10th year can be made for an
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infinite period Now formula used what what
are the formulas we have to use in this are
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now F to A future value to annuity this is
A is equal to F A by F i N and this formula
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this one is equal to F into 1 i divided by
1 plus i to the power N minus 1 and present
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value of a perpetuity
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is equal to PV is equal to A by i now let
us apply this in different numericals
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Now objective one given the capital investments
at different time line attractive rate of
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return unequal estimated life span of capital
investment annual operating cost compare two
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different investments based on capitalized
cost method For example one two different
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alternatives A and B are available to supply
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Example one two different alternatives A and
B are available to supply water to a remote
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area of Aligarh which is comparatively arid
from mountains of Himalaya In alternative
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A a pipeline can be laid down a pipeline can
be cost
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this is hundred crores will be required measure
or overhauling every 10 years costing this
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is 1000 crores100 crores overhauling is 100
crores 10 years every 10 years and annual
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up keeping cost of the pipeline is 10 crores
per year
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Now for the B to construct a canal from the
Ganga river to a Haridwar to Aligarh costing
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1500 crore overhauling cost is 60 crore every
12 years up keepng cost is 15 crore per year
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and the value of i is 10% Now one crore is
this so let us analyze this and suggest which
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alternative I should select based on the perpetual
cost method
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So solution alternative A
capital cost of pipeline is equal to 1000
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into ten to the power seven rupees one-time
capital cost of hundred crores required overhauling
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over 10 years so perpetuity will be perpetuity
will be annuity of future value of hundred
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crores
taking N equal to 10 divided by i So what
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I have to do this hundred crores is a future
value but as after 10 years I have to spend
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hundred crores
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So I have to find out the annuity of this
100 crore that means annuity of a future value
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taking N equal to 10 and then divided by i
so this comes out to be hundred into 10 to
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the power seven into i divided by i into one
plus i to the power N minus I this is the
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formula And if I solve this this becomes hundred
into 10 to the power seven into 0.627453 equal
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to 62.7453 into ten to the power seven
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So this perpetuity of this that means if I
spend this much of money then I will get enough
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money to spent one hundred crores every 10
years Now one time capital required for paying
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10 crore annually perpetually equal to ten
divided by 0.1 which is the value of i becomes
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hundred crores As the total capital required
from the project to run it perpetually for
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a this is 1000 into 10 to the power 7 plus
62.7453 to the power seven plus 100 to the
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power seven
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This comes out to be 1162.7453 crore similarly
for alternative B we can calculate now the
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capital cost
is equal to 1500 into 10 to the power seven
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one-time capital required for overhauling
every 12 years is equal to 60 into10 to the
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power seven into i divided by i one plus i
to the power N minus one this value This comes
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out to be 60 into 10 to the power seven into
0.467633 equal to 28.057989 into ten to the
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power seven
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Now one-time capital required one-time capital
required for paying rupees 15 crore annually
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perpetually equal to 15 divided by i equal
to 15 divided by point one equal to hundred
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fifty crore So total capital required here
in the case of B is fifteen hundred into 10
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to the power 7 plus 28.057 into 10 to the
power seven plus hundred fifty into ten to
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the power seven is equal to 1678.057 crore
So as the alternative A requires less capitalized
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cost this than the alternative B it should
be selected
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This is example two two plans A and B exist
for building construction for plan A an total
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initial investment of sixty lakhs is required
for which forty lakhs will be spent on permanent
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construction and the rest 20 lakhs will be
spent immediately on temporary structure which
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will require renewal every 15 years The annual
operating cost of plan A will be rupees 50000
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every year However for plan B an initial investment
of 40 lakhs is required of permanent nature
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In addition to it an additional investment
of rupees 30 lakhs on a permanent structure
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is required after 10 years from now The annual
operating cost of Plan B is rupees 20000 per
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year If attractive rate of return is 10% land
is free of cost and is not be included in
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computation then using capitalized cost method
find out whether you will prefer plan A or
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plan B
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This numerical we have solved using other
methods also so let us solve it Initial capital
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investment equal to forty lakhs capitalized
cost of the temporary structure of 20 lakh
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will stay for 15 years So initial capital
investment that will produce 20 lakhs each
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15 years perpetually this can be given by
20 lakh into i divided by i into in bracket
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one plus I
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this I am converting my initial investment
that is P to A
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So this will be 1 minus 1 plus i to the power
minus 15 and this comes out to be rupees 2629475.538
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Now please note that 20 lakhs is the present
worth value of the investment as it is done
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at the same time as the investment 40 lakhs
that means in the timeline t equal to zero
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here I am investing 40 lakhs plus 20 lakh
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So this is the initial value here 20 lakh
and this initial value 20 lakh the present
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value has to be converted into annuity and
that annuity has to be divided by i to convert
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into perpetuity So this is done like this
now capitalized cost of up keeping
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is equal to 50000 divided by i equal to five
lakh So the net capitalized cost 40 lakh plus
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2629475.538 plus five lakh which comes out
to be rupees 7129475.538 so here we write
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down net capitalized cost for A is equal to
rupees 7129475.538 similarly for plan B I
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can calculate
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Initial capital investment equal to 40 lakhs
capitalized cost of
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the temporary structure costing rupees thirty
thousand lakh each 10 year from now perpetually
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is equal to 30 lakhs into i divided by i into
one plus i to the 10 minus one Now why we
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will see that this formula has changed in
compared to the first one because at the first
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one that 20 lakh was the present value here
the 30 lakh is future value
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So we are converting a future value to annuity
and thatâ€™s why this formula has changed
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and this comes out to be rupees 1882361.846
Now the capitalized cost for up keeping amount
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rupees 20000 each year is equal to 20000 divided
by i is equal to 20000 divided 0.1 equal to
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two lakh Now if we add net capitalized cost
for B is equal to 40 lakh plus this value
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1882361.846 plus these value two lakh and
this comes out to
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be 6082361.846
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Now as the net capitalized cost for plan B
is less than plan A plan B is selected for
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investment so this is selected for investment
To summarize we have seen that the perpetuity
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or capitalized cost method can solve solve
some problems easily depending upon the situation
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of the problem and data of the problem And
here we have seen that how to apply this technique
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for alternative investment that is perpetuity
or capitalized cost method Thank you