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 the present lecture we will
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take minimum return as a cost method for alternative
investment selection minimum return as a cost
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this is an alternative analysis method in
which minimum acceptable return is included
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as a cost for each alternative and then the
annual profit and savings are calculated for
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all alternatives
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The alternative which provides maximum savings
over and above the minimum acceptable rate
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of return which is incorporated as a cost
in the formulation is selected An example
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is included in this unit to demonstrate the
method
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Now this is the formula used where the P is
converted into A that is present value is
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converted into annuity and this formula will
be used in the present lecture Now the objective
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giving the capital investments estimated
life span of capital investments annual operating
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costs and annual earnings MARR compare four
different investments based on minimum return
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as a cost method for the selection of the
best investment
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This is the first question that is example
number one tells there are four different
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Plans under consideration for construction
of buildings for a commercial purpose to earn
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rent A comparison of these Plans to be made
at the end of time window of 20 years at that
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time assume that the resale value is 200 percent
of the original investment It is estimated
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that the minimum acceptable rate of return
that is MARR as well as interest rates are
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10percent The data for the above Plan is given
in the table below
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So Plan A
Plan B Plan C and Plan D Plan D Original investment
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is equal to 110000 one lakh ten thousand this
is 201000 that is 300000 and this is 480000
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Annual rent is 20000 that is 35000 this is
58000 and this one 109000 annual maintenance
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2000 5000 8000 and this is 10000 taxes 1000
1500 1800 2000 As after 20 years the investment
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will fetch double the amount and will result
a profit of hundred percent
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This amount which is a future worth of profit
should be distributed as a annuity throughout
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the 20 years period and should be treated
as earning So it tells that now the investment
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which will be done here at t equal to 0 after
20 years this value will double and hence
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I will get my profit here that 100 percent
profit here and this profit which is a future
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value has to be distributed as annuity
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So for that the original investment needs
to be recovered through an annuity and should
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be treated as expenditure So a let us start
analyzing it Annual profit due to 200 percent
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enhancement of cost Plan A so the profit will
be 110000 this price which is 110000 rupees
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will be double here after 20 years so my profit
is 110000 rupees
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So this is a future value which has to be
converted into annuity using the formula So
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this is the formula one plus i to the power
20 minus one so this comes out to be rupees
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1920.56 So here the profit for A Plan is 110000
rupees for the B Plan will be it will be 201000
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for the C Plan it will be 300000 and for the
D Plan this will be 480000
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Now the same thing for Plan B annual profit
due to to enhancement of cost for Plan B this
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will be 201000 into the same factor 0.1 divided
by 1 plus 0.1 20 minus 1 is equal to rupees
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3509.38 Now for Plan C same thing for for
Plan C will be equal to 3 lakh into 0.1 divided
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by 1 plus 0.1 20 minus 1 and this comes out
to be rupees 5237.88
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So now for D Plan for Plan D this when calculated
comes out to be rupees 8380.62 Now this is
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the profit which has been converted into annuity
and so this is the receipt Now the same thing
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can be done for this investment original investment
the original investment which is a value has
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to be converted into annuities So this is
this is basically a present value here we
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are converting the future value and when will
be converting the original investment as it
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is a present value it will be converted to
annuity with some other formula than what
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we have used here
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Now when we are converting it to annuity basically
the investment is here for Plan A this investment
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is 110000 rupees for Plan A So this is a present
value which has to be converted into annuities
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so annual cost of capital recovery this is
for Plan A this will be equal to the value
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110000 into 0.1 divided by 1 minus 1 plus
0.1 to the power minus 20 because my time
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window is 20 years
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This comes out to be rupees 1292056 similarly
the annual cost of capital recovery for Plan
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B is equal to the cost of the which is 201000
rupees into the same factor is 0.1 minus 20
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This comes out to be rupees 23609.38 Similarly
we can find out for Plan for Plan C this is
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300000 into same factor 0.1 1 minus minus
twenty is equal to rupees 35237 thirty five
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thousand two thirty seven point eight eight
and the same thing for Plan D comes out to
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be Plan D comes out to be rupees 56000 56380.62
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So this is not earning this is a investment
we should remember it The annuity of profit
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is 1920.56 this is 3509.38 this is 525237.88
this is 8380.62 Now annual cost cost of capital
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recovery is 12920.55 this is 23609.4 that
is 350237.88 this is 560380.61 Now net annual
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profit
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net annual profit is equal to 1920 for Plan
A
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for Plan A this is 920.56 plus 20000 minus
12920.56 minus 2000 minus1000 it comes out
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to be rupees 6000
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Now if I see the numerical this 1920.56 has
come from here because this is a receipt and
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then annual rent for Plan A is 20000 so this
annual rent for Plan A Then this is the annual
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cost of recovery and so this is a negative
quantity because this is the spending so this
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is my negative and then annual maintenance
is 2000 so it’s a negative quantity and
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taxes is 1000 so this is negative quantity
So these are two receipts and this we have
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to give this is a expenditure from year to
year is expenditure this is recipient so profit
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is six thousand
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So similarly for all the Plans I can calculate
the net annual profit
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so this is 6000 this is 8399.98 this is 18200
this is 49000 Now annual savings after adding
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MARR as cost if I calculate return this comes
out to be a 5.45 percent this is 4.179 percent
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This is 6.07 percent this is 10.20 percent
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Now here if I calculate annual
savings after adding MARR as a cost
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this will be equal to 6000 which is my net
profit minus 0.1 because 10 percent is MARR
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So ten percent of the cost original cost of
the equipment for the Plan this is 110000
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so 10 percent cost of this is reduced from
here then it gives us minus 5000
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Let us check it this is correct so I get minus
5000 So
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if I make a column like this annual savings
after adding MARR as a cost this becomes minus
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5000 this becomes
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That means this quantity which shows minus
signs So that these Plans will not generate
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a profit of 10 percent while Plan D will generate
a profit of more than 10 percent and if we
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compare the returns we find that this 5.45
percent which is less than 10 this is 4.179
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this is less than 10 and this is also less
than then and this the only Plan which generate
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profit more than 10 percent
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So my conclusion is the annual savings after
adding MARR as a cost is maximum for Plan
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D hence it is selected for investment The
annual savings after adding MARR as a cost
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for Plan A B C shows a negate value indicating
that it offers a return which is lower than
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MARR and hence these Plans cannot be consider
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Now let us take an example example two example
two shows the there is proposal to pump crude
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oil using a pipeline For this process three
pipeline diameters 150mm 200mm 457mm and 610
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mm have been selected It is a known fact that
if one selects higher diameter pipeline its
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fix cost will be more however it’s pumping
cost will be less The problem thus turns out
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to be the selection of most economic diameter
If the service life of pumping station and
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pipeline is 18 years with some salvage value
that is 10 percent of fixed cost can be consider
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salvage value is 10percent of the fixed cost
of the pipeline and minimum acceptable rate
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of return MARR is 10 percent
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Then we have to select the best pipeline diameter
These table shows you the complete data of
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the all the four diameter of the pipelines
And distribution of data is also given like
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a total fixed cost is distributed amount the
investment in pipeline number of pumping stations
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required cost of a single pumping station
all these add together gives you the total
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fix cost Similarly taxes insurance inspection
maintenance of pipeline attendant cost electricity
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bills will give you total annual cost
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So here I will only write the total fixed
investments and total annual cost and the
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distribution of all these costs are given
in this table So pipe A this is example two
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pipe A which is 150 mm diameter pipe B which
is 300 mm diameter this is D equal to diameter
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equal to this pipe C this is 457 mm diameter
and pipe D which is 610 mm diameter Now total
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fixed investment
total fixed investment in rupees is 285000
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this is 315000 this is 355000 this is 420000
and total annual cost which is a summation
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cost including taxes maintenance of pipeline
attendant cost electricity bill etc is 95000
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91000 and 84000
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Now we have to use the minimum cost as a return
method to select which pipeline I should go
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for So depreciation of the pipeline
using straight line method is equal to this
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is for pipe A is equal to 285000 1 minus 0.1
divided by 18 which comes out to be 14250
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Now how this has come basically this depreciated
amount will be this minus this salvage value
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So if I open up this this is nothing but 285000
minus 0.1 into 285000 Now this gives me the
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salvage value this is my original cost a
divided by this is my service life
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So obviously this will give rise to the depreciation
the value of a depreciation is 14250 rupees
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Now annual savings
after including MARR as a cost is equal to
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now if you see the annual earnings here these
annual earnings is 130000 this is 130000 this
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is 130000 this 130000 this is same because
all the pipelines will do the same job so
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they will be rewarded same
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So this is equal to 130000 this my earning
then my expenditures expenditures will be
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the depreciation 14250.00 minus this is my
annual cost 95000 minus 0.1 into 285000 This
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is what this is MARR and this is my fixed
cost original cost cost so what I have done
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I have presumed that at least the pipeline
should earn 10 percent of the fixed cost as
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a return
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So this return I am subtracting from here
and when I subtracted I found this is minus
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7750 That means this pipeline is not going
to give me 10 percent return Even if this
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value become zero I will get a 10 percent
return as this value is minus I am not going
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to get to 10 percent return and hence the
this is rejected
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Similarly
if I compute for others now depreciation cost
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for pipeline B will be equal to 315000 into
1 minus 0.1 divided by 18 comes for 15750.0
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and annual saving including MARR as cost this
is 130000 minus 15750.0 minus 91000 minus
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0.1 315000 and this comes out to be minus
8.50 Again the pipeline B is not giving me
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a return of 10 percent This is MARR as a cost
this has been included so even if I get zero
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value here my return will be 10 percent As
I am getting a negative value this pipeline
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will also not able to give a return of 10
percent
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So if I calculate for the rest two pipelines
this result so this is the table whcih shows
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me the complete results So annual savings
annual savings
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this is minus 7750 this is 8250 this is 1250
this minus 17000 so except pipe C all are
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giving negative that means they are not giving
me 10 percent return
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So as pipe C is giving more than 10 percent
return this would be selected for the job
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So to summarize this in this lecture we saw
the minimum return as a cost method and how
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to apply this method for selection of alternative
exclusive alternates and we have seen that
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this is very simple method and can solve complicated
problems Thank you