WEBVTT
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Welcome to the course Depreciation Alternative
Investment and Profitability Analysis Today’s
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lecture we will start the module 2 that is
alternative investment and in this alternative
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investment will take Annual Cost Method So
in this lecture I will introduce to the Alternative
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Investment and Annual Cost Method Alternative
Comparison or Alternative Investment the common
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problems confronted in engineering economics
are those where alternative comparison between
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two or more mutually exclusive alternative
investments compete involving different series
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of capital disbursements
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For example if one alternative have both less
capital investment as well as operating cost
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there is no need of comparing it with other
alternative However the comparison becomes
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essential if one alternative offers higher
initial capital investment but lower annual
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operating cost in the successive years in
comparison to the second alternative which
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offers less capital investment initially but
subsequently higher operating cost
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In such cases one has to find trade-off between
the future advantages of a lower operating
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cost vis-a-vis disadvantage of higher initial
investment where different series of disbursement
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are compared it is necessary to reflect the
time value of money under each alternative
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A variety of methods exists for selecting
the superior alternative from a group of alternative
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proposals Each method has its own merits and
applications
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The present module demonstrates how to apply
the profitability measures to select the best
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alterative out of a set up mutually exclusive
alternatives properly Mutually exclusive alternatives
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means that the selection of one alternative
excludes the consideration of any other alternative
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Now in the these lectures we will cover Annual
Cost Method 1 and 2 Present Worth Method Perpetuity
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Method Rate of Return Method Incremental Rate
Of return Method Minimum Return as a cost
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Method So all these methods will study in
this course Annual Cost Method which is the
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topic of this lecture in engineering economics
the annual cost method or equivalent Annual
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Cost or Annual Worth Method is the cost per
year of owing and operating an asset over
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its entire life span
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This method is often used as a decision making
tool in capital budgeting when comparing investment
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projects of un-equal life spans is required
For example suppose if event A has an useful
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life of 11 years and that a project B is 15
years it could be inappropriate to simply
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compare the net present value of both projects
unless neither project could be repeated
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Now let us see how to derive the formula for
annual cost method Now in this slide before
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you it is given I am explaining this basically
if I draw a timeline at timeline t is equal
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to zero a investment is done an investment
is done here Now this is the time when the
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property retires so annual cost method converts
this depreciable amount into a series of payments
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whose when present value is calculated when
all these payments when converted into its
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present values and add up then we find that
the whatever value I have invested at t is
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equal to zero equals the summation of all
present values
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So annual cost can be calculated with this
present cost of asset into rate of interest
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divided by 1 minus 1 plus rate of interest
to the power minus useful service life So
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basically this is a annuity so you can use
the annuity formula A is equal to p i 1 plus
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i to the power N divided by 1 plus i to the
power N minus 1 and when this is simplified
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then we get a formula A is equal to p i 1
minus 1 plus i to the power minus N
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This is the formula
or we can use this also as well for calculation
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of annuity which is an annual cost in the
present case Present value and net present
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value have a serious flaw when it comes to
making comparison between available investments
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The flaw lies in the fact that you must set
that opportunity rate a fixed rate to be used
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over the investment life and as we noted that
opportunity rate must reflect comparable risk
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for comparable investments That means you
fix a quantitative calculation based heavily
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on a quantitative qualitative judgement in
comparing two investments a mistake or inaccuracy
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in the opportunities cost that is discounted
rate will lead to a distortion of present
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values
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Now we take an example now the objective of
this example is given the capital investment
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zero salvage value attractive rate of return
equal estimated life and different annual
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operating cost Compare two different investments
based on annual cost method So in the example
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no 1 the data for two machines are given Select
the appropriate machine based on annual cost
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method So
machine A
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machine B capital investment this is 45000
this is 30000 useful life N is 10 years 10
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years operating cost
is equal to rupees 8000 per year and this
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is rupees 15000 per year and i is 10 percent
and 10 percent and our aim is to find out
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using annual cost method that which machine
I should select
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Now the annual cost of a the capital recovery
is the annuity based on time value of money
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that one has to pay throughout the useful
life of the machine which will be equal to
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the capital cost of the machine at the start
of the first year that I had already told
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you So annual cost of capital recovery annual
cost of capital recovery is equal to capital
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investment into i 1 minus 1 plus i to the
power minus N this is the value So for A if
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I calculate this then it is equal to for A
the annual capital recovery is equal to 45000
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into 0.1 divided by 1 minus 1 plus 0.1 minus
10 to the power minus 10 which comes out to
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be rupees 7323.54
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Similarly for B if I calculate the annul capital
recovery factor then this is 30000 into 0.1
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divided by 1 minus 1.0.1 minus 10 is equal
to rupees 4882.36 and this is per year and
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this is per year So if I keep this value here
7323.54 and 4882.36 so what basically I have
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done
that I have converted this capital cost whose
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life span is 10 years into a per year cost
Now so annual cost will be basically the addition
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of this and this If I add these two this becomes
rupees 5323.54 and if i add this and this
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then it becomes rupees 19882.36
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So what we find that machine A is cheaper
because its cost is 15343.54 whereas the cost
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of the machine B is 198082.36 and hence our
selection will be machine A so we will go
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for machine A This selection we have made
based on annual cost method
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Now this is a table I had given to show that
if the present value of all the instalments
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are calculated comes out to be the original
cost of the equipment at t equal time equal
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to zero that is for A machine it is 45000
and for B machine it is 30000 I have calculated
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for A machine only so it is 45000 Now let
us take the second problem there is data of
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two machines A and B are given below
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Data for two machines A and B are given below
Plot how the net present worth or for both
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machines A and B vary with variation in minimum
acceptable rate of return from 6 percent to
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30 percent Now here I have again two machines
now the capital investment is 10000 here here
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8000 now useful life is 10 10 here savage
value 0 0 here operating cost is 3000 and
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here 3500 Now rate of return is 15 percent
here 15 percent now you have to select machine
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or A or machine B based on the annual cost
method
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So basically this cost is per year and this
cost is for 10 years so I have to convert
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this cost into per year cost using annual
cost method and then I can add this with this
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to find out the total annual cost and based
on the annual cost I will take a decision
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Then let us see now annual of capital recovery
for A is equal to 10000 into 0.15 the value
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of i 1 minus 1 plus 0.15 to the power minus
10 Now this comes out to be rupees 1992.52
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and this unit is per year
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So the total annual cost that means per annum
how much I am spending is equal to rupees
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1992.52 plus this operating cost which is
per year basis 3000 it comes out to be rupees
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4992.52 So this is N1 cost of capital recovery
is 1992.52 and while I add this with this
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this becomes rupees 4992.52 Similarly capital
recovery for machine B would be 8000 and this
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come out to be 1594.02 so this is 1594.02
plus 3500 and this comes out to be rupees
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5094.02
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So this is 1594.02 and we add this becomes
rupees 5094.02 this plus this
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So as the annual cost of the machine A is
less than machine B so my selection will be
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A based on annual cost method
So summarizing the lecture in this lecture
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I have introduced the concept of alternative
investment and one of the methods for achieving
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the alternative investment which was annual
cost method has been introduced but some part
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of annual cost method has been introduced
in the lecture number 2 of this series that
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is module 2 will see more problems on annual
cost method Thank you