WEBVTT
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Welcome to the course Depreciation Alternate
Investment and Profitability Analysis We are
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continuing with the module 3 that is profitability
analysis Today’s lecture is devoted to return
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on investment return on investment this is
a profitability measure and is measured as
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the ratio of profit to investment A high return
on investment means the investments gains
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compare favorably to investment cost although
several measures of profit and investment
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could be used the most common are net profit
and total capital investment
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As a performance evaluator ROI that is Return
On Investment is used to evaluate the efficiency
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of an investment or to compare the relative
efficiency of a number of different investments
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ROI is equal to Np by F where ROI is the annual
rate of return on investment expressed as
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a fraction or percentage per year Np annual
net profit and F as total capital investment
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ROI method does not use the concept of time
value of money Now let us see the formula
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which is used for the ROI computation If net
profit is not constant year to year and similarly
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if additional investment is carried out in
the life span of the project then ROI becomes
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1 by N summation j equal to N to N Npj divided
by summation j equal minus b to N Fj
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Where N stands for the evaluation period of
the project Npj is a net profit in the jth
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year minus b is the year in which the first
capital investment is made In general capital
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investment is made before the start of the
production and Fj is the total capital investment
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done in jth year
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Now let us derive some terms net profit is
equal to revenue minus all expenses minus
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income tax
all expenses
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is equal to cash expenses plus depreciation
Income tax is equal to revenue minus all expenses
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into tax rate Now net profit
is equal to revenue minus all expenses
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minus revenue minus all expenses into tax
rate this is basically income tax is equal
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to revenue 1 minus tax rate
minus all expenses 1 minus tax rate
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This is equal to revenue 1 minus tax rate
minus cash expenses plus depreciation into
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1 minus tax rate This is equal to revenue
1 minus tax rate minus cash expenses 1 minus
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tax rate minus depreciation 1 minus tax rate
Cash flow cash flow is equal to net profit
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plus depreciation or cash flow if you can
write down is equal to revenue minus tax rate
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minus cash expenses minus 1 minus tax rate
minus depreciation into tax rate or cash flow
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is equal to revenue 1 minus tax rate minus
all expenses 1 minus tax rate
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plus depreciation
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Now these are some derivations now net profit
of a project are not generally constant throughout
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the life span N of the project In such cases
an average ROI called averaged rate of return
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is used so average ROI rate of return is equal
to average annual profit after tax into 100
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divided by investment over the life span of
the project So average ROI is equal to 1 by
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N summation j equal to 1 to N Npj divided
by j equal to 1 to N Fj There is another similar
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method profitability method called Average
Rate of Return ARR Though there are many alternative
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methods for calculation of ARR the most commonly
used definition of ARR is as follows
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ARR average annual profit after tax into 100
divided by average investment over the life
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span of project Now the average profit is
computed by adding expected yearly profits
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after tax for the life period of the project
and then divided the result by the life of
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the project Now average in investment in this
case is computed as
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net working capital plus salvage value
plus 0.5 into initial cost of the machine
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of project minus salvage value So based on
ARR obviously the project having higher ARR
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will be preferred to project with lower (a)
ARR This method does not use the concept of
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time value of money
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Now let us take example 1 an investor by stocks
worth 10000 cost of stock is equal to 10000
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and sells it after 1 year at a value of 15000
if he pays the income tax at the rate of 15
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percent
then calculate return on investment Now initial
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solution initial investment equal to rupees
10000 gross profit after a year is equal to
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15000 minus 10000 equal to 5000 now net profit
is equal to 5000 into 1minus tax rate is equal
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to 5000 into 1 minus 0.15 this comes out to
be rupees 4250 So ROI is equal to 4250 into
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100 divided by 10000 comes out to be 42.5
percent
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Now take another example now the objective
of the example is given the initial investment
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and yearly non-uniform cash inflow after tax
compute the return on investment Now here
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example 2 two mutually exclusive projects
C and D have similar initial costs rupees
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50000 their cash inflow after tax are given
in the side table Determine the return on
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investment for both projects So we take example
2 initial cost cost of project C and D is
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equal to rupees 50000 Now cash inflow
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project C project D this is 1 2 3 4 5 6 7
8 this is 12500 14200 15000 8300 48000 2000
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1100 and 0 and this is 9980 10000 9720 9300
11000 12000 14000 14800
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Now specialty of this is that after this 15000
this is decreasing almost very marginal cash
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inflows to the project C whereas project D
is consistently doing better Now if I use
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this method you will remember that we have
used this method in payback period and we
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have reached to a wrong conclusion Now let
us see this example is giving us the right
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selection or not Now average ROI average annual
profit after tax into 100 divided by investment
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over the life period of project
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So average ROI of project C is equal to 12500
plus 14200 so and so forth up to 1100 divided
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by 8 divided by 50000 Now this comes out to
be 57900 divided by 8 divided by 50000 this
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gives 14.48 percent So we got for project
C
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C average ROI is equal to 14.48 percent
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Now if I compute this for D project D average
ROI is equal to for project D average ROI
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is equal to 9980 plus 10000 dot dot dot this
is 14800 divided by 8 divided by 50000 (())(22:27)
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into 100 year then only the percentage will
come out And this comes out to be 90800 divided
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by 8 into 100 divided by 50000 this comes
out to be 22.7 percent So this is 22.7 percent
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so obviously my selection will be project
D As the average ROI of the project D is more
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than the project C and hence the project D
is better
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Now please note that the above decision is
contrary to the decision taken in example
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3 of payback period please also note that
the method does not use concept of time value
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of money and thus does not adjust the profit
with time
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Now we go to the example 3 the objective of
the example 3 is given the yearly non-uniform
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investment and yearly non-uniform cash inflow
and the percentage of tax compute the return
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on investment The example 3 is the investment
and profit of two mutually exclusive projects
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C and D are shown in table and if the tax
is 30 percent determine the return on investment
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Now the projects are cash inflow this is minus
2 minus 1 1 2 3 4 5 6 7 8 this is project
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C this is project D now this is 0 0 because
I will not get profit profit starts at 1 now
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this is 2200 sorry 22000 this is 20345 this
is 18760 this is 17890 this is 15670 this
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is 11000 this is 10000 and this is 0 this
is 0 0 here this 23000 this 19900 this is
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17690 this is 16543 this is 54060 this is
14340 this is 14000 this is 14800 Now if you
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see the
investment cash flow now at minus 2 you will
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remember that I was summing the investment
with j is equal to minus b and there I have
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explained that that this when the profit starts
before that the investment takes place and
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due to that this minus 1 and minus 2 are coming
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So it is minus 2 years my investment projects
C project D this is 50000 this is 5000 minus
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1 this is 5000 this is 50000 50000 this is
6000 now at fourth year this there is a investment
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4500 and here there is a investment 3200
rest three digits are 0 0 0 0 here 0 0 0 and
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at the end here there is a investment of 2100
then 0 then investment of 2300 here two zeros
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here three zeros Now this is the scenario
so there are different investments at different
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time lines and there are different receipts
in different time lines
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If it is so then how to compute the return
on investment Now for
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this solution N is equal to 8 years so ROI
is equal to (am) average annual profit after
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taxes into 100 divided by investment over
the life period of the project this I have
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already shown you
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So annual profit for project C
the annual profit is equal to 20345 plus 18760
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and basically now the annual profit for project
C is now you write down all these figures
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that 22000 plus 20345 plus 18760 plus dot
dot dot it goes up to this 10000 10000 this
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comes out to be 115665 this is annual profit
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So annual profit after tax after tax will
be 115665 into 1 minus tax rate which is 0.3
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because 30 percent tax is there So remaining
is 1 minus 0.3 0.7 into this so this is remaining
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amount after tax comes out to be rupees 80965.5
Now the investment these are the investment
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figures if I add them together 50000 plus
5000 plus 4500 plus 2100 comes out to be rupees
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61600 Now average annual profit
the profit has to be divided by the project
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life span that is 8 8 So this is 1 by N into
80965.5 now ROI is equal to now 1 by 8 into
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80965.5 divided by so into 100 divided by
61600 this comes out to be 16.42 percent
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Now similarly for project D also I can compute
project C ROI is equal to this
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now project D ROI I have to calculate this
is annual profit is equal to addition of all
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these numbers 23 23000 plus dot dot dot up
to 14800 this comes out to be rupees 135733
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135733 So
annual profit after tax is equal to rupees
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135733 (1 minus 0.3) it comes out to be rupees
95013.1 Now investment obviously this figure
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is investment so that is five 50000 plus 6000
plus 3200 plus 2300 this comes out to be 61600
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again So average ROI sorry average annual
profit
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annual profit is equal to my profit after
tax is this so 1 by N into 95013.1
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So average ROI if I calculate this becomes
1 by 8 into 95013.1 into 100 divided by 61500
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this is investment is (61 thou) let me check
the investment (())(35:10) 56000 plus
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3200 plus 2300 61500 so this is 61500
basically So this is 61500 and comes out to
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be 19.31 percent this is 19.31 percent So
we have computed up to example number
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3 Let us summarize we are dealing with the
profitability analysis in this lecture and
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in the profitability analysis we have
gone for the return on investment
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Now in the return on investment we have seen
three examples and in one example which
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were solved for the payback period as well
as return on investment we saw that the return
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on investment gives better results in comparison
to the payback period thank you