Modified Internal Rate of Return (MIRR) is presented as a superior investment appraisal technique compared to traditional Internal Rate of Return (IRR) because it addresses IRR's practical limitations and provides more reliable financial insights.
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So for modified IR it's an improvement over
over
the traditional IR that you know. So
which means what the modified IR tries
to do is to
cater for those weaknesses of
traditional IR. And if you recall those
weaknesses that we learned in FM, the
first one is the fact that under the
traditional IR
there's an assumption that all the cash
flows that a project generates all those
cash flows are invested at IR a constant
rate and we know that this is not
practical because IRRa is like an
indication of your cost of capital. So
you cannot say the cost of capital is
the same thing as investment rate.
Your financing rate is your cost of
capital. So if there are cash outflows
that is the money you have kind of
borrowed. So it makes sense to use a
financing rate for that. But the inflows
that you are generating cannot be
reinvested at the same rate. It is not
practical and that's a weakness that MR
will cover. Likewise,
if you look at a project, there's a
possibility that a project will have
more than one IRRa. And that is why we
say that the traction does not give a
unique figure because you can have more than
one IRR
and that that is a confusion.
That's another weakness that MR has come
to fix. And likewise, IRRa is not a
because even if your IRRa says it's 10%,
it doesn't mean that the return on that
investment is 10%. So because of that is
just difficult to interpret
especially for nonac accountant.
And also sadly actually
this traditional might contradict NPV
decision. So it might give a contradictory
contradictory
result. So IR might be saying don't do
the investment NPV saying do the
investment. Remember what we learned in
FM is that if there is such
contradiction NPV supersede. So another
NPV decision.
decision.
So all these are weaknesses of
traditional IR and that is why we now
have MIR
which is a modified version that
that
actually makes life easy for you because
for MR interestingly
it's a return measurement. So if you get
MR of 10% return on investment is deemed
to be 10%. It will never contradict NPV.
It is unique and it doesn't make this
constant rate assumption for both inflow
and outflow. For MR you can work with
two rates, two different rates. All the
inflows are invested at reinvestment
rate and all the outflows are discounted
at the financing rate. And you will see
an example which we're going to do.
Yeah, but in terms of decision is the
same as what you have in IRRa. You make
a decision whether to do an investment
or not when M IR is greater than cost of
capital. Remember this is similar to
what you had for traditional IR because
the decision to do investment is done
when IR is greater than cost of capital.
So that is just the similarity between
both uh methods.
Now the next question is how do we
calculate M IR?
How do we calculate? What is the
formula? And there are two formulas I'm
going to show you. But I'll start with the
the
simple one which you normally see in
your ACC exams. They will give you the M
formula to be equals to
the present value of your inflows or the
investment or the return cash flows.
I'll call it inflows to make it simple
raised to power 1 / n
* 1 + cost of capital
This is a popular formula you will see
in exams. However, this formula is
hardly useful. Yeah. Because this
formula only works
only when
the cost of capital is the same as
reinvestment rate.
So what we are saying is that the cost
of capital is the same thing as the rate
you need to use to reinvest the inflows
that the project is generating. Yeah.
You can have a question like that but
it's real. Yeah. Because then it makes
no difference from what we've been
learning because the reality is
MR is really really useful when you have
some complications. I mean such that you
are able to account for different
reinvestment rates from the cost of
capital right
and we're going to work some examples
which um remember R is cost of capital N
is the number of years deter of the
project and if you just to work an
example quickly for you to see how you
can apply this formula let's say you
have year zero you have year one cash
flow year two cash flow year three and
year four. So, initial outlay of 20,000.
You have 8,000 inflow in year 1, year 2, 12,000.
12,000.
Let's see. You have 4,000 here and
2,000. So, let's say a project with a
cost of capital of 8%. And for this one,
we're going to assume that this cash
flows of 8,000, 12,000, 4,000 are all
reinvested at the same 8%. So, which
means the cost of capital and the
reinvestment rate are both the same. In
that case, we can apply this formula
here. So, that's what I'm going to use
now. So first of all we need to
calculate the present value of all the
cash flow which means we need a discount
So we look at the PV table. We need to
pick the discount factor for at 8% for
year 0 we know it's going to be 1
and uh for year 1 that is 0.9
2 59
year two no I'm looking at anointed
I need the PV
Yes. So for year 1 under 8% you have 0.92
0.92
and for year one it's always going to be
0
two will be 0.8 8 573
zero. Okay.
So we know the discount factor. So we
can now get the present value 20,000 * 1
that remains 20,000.
Then we have 8,000 * 92
92
8,000 * 9259
that gives 7 4 07 12,000
12,000
multiply by85 73
73
that's 10
Then 4,000
multiply by.7
9 38 3175
and 2000 * 735
735 470.
So we have the PVs for all the inflows.
These are the four of them and we have
the PV for the outflow as well. So we
need to add all of these together
to get the PV of inflows total.
And if you add all of that together
quickly, plus 3175
+ 747.
That gives us 22
339 22 339.
339.
So that's the PV of all inflows. So we
go back to our formula. This formula we
need to apply it now. So which means
you're going to have equals to 22 339
/ 20,000. So you can ignore the negative
of the cash outflow in this formula. The
tenure of the project is four years. So
1 / 4 * 1 + 8%
everything minus 1. So let's deal with
this part quickly. So 22339 / 20,000
that gives 1.117.
1 / 4 * 1.08 08
10 - 1.
and then multiply by 1.08 08 that gives
us 1.11
then minus one that give us 0.11
Remember
the formula that we have used here is only
only
applicable when the cost of capital is
the same as reinvestment rate. When it
is different, you need to use a
different approach which is much more
realistic and that is the approach to
that I want to teach you now. Yeah. So
please pay attention to this approach to
to MR.
In this case the formula is different
and the formula is
is
no more present value for the inflows
but rather the terminal value of the inflows
inflows
divided by the present value of the
outflows. So add flows remains the
present value.
Then all of that
raised to power 1 / n minus one. So you
can see the formula is a bit shorter but
you still need to understand how you
apply it. Remember TV means terminal
value. Please take note.
So which means you need to learn how to
calculate terminal value. Terminal value
is just from the word terminal. terminal
means at the end. So you are saying for
every cash that we generate take for
instance this 8,000 what is the value at
the end because for this project that is
4 years the end of the project is end of
four years
this point. So we want to calculate the
terminal value you're going to be asking
yourself this 8,000 what will be the
value at year four? So which means you
will need to reinvest it once you make
this 8,000 in year 1 you invest it year
2 1 year 2 years 3 years. So you're able
to invest it for 3 years but at
reinvestment rate. So this time around
it's still going to be at 8%. 12,000 you
reinvest for 2 years, 1 year, 2 years.
4,000 you invest just one year and 2,000
you don't have time to reinvest because
it's just coming in year four. So if we
want to use that
understanding to test this formula. So
it means we need to calculate the
terminal value of all the inflows.
So which we're going to start with the
first one 8,000. So for the 8 for year 1
the terminal
cash flow for year 1 will be 8,000
invested at 8% for 3 years raised to
power 3. So we need to know what that
will be quickly.
The same thing we do for year two. Year
two we're going to invest. How much
would we make? We're going to make
12,000 in year two, but we're only going
to invest it over two years. We only
have two years left,
but still at the same 8%. Raise the
is just um 4,000
and yet four is 2,000. This one we don't
have time to reinvest it. So this one
remains 2,000. This one will we can
reinvest just for one year at 8%. So
let's see. So 1.08
raised to power 3
multiply by 8,000 that will be the
terminal value of 8,000. So which means
this 8,000 that we made in year 1 if we
reinvest it at the 8% by year 4 that
will be the value. The same thing we'll
* 12,000
becomes 13 996.
996.
Then the last one * 4,000
that's 4320.
So we now need to add all the terminal
cash flows together to get
what the total terminal value of all our
that gives 30 393.
393.
So now we know this part. We also know
PV of outflows because it will remain
20,000 because there's no outflows
during the year which is possible and
I'm going to work an example with that.
But for this question the outflow is
just beginning of the year. So the P
remains 20,000.
So which means we can just apply this
formula easily and that means our mirror
will be equals to 30 393
393
/ 20,000
raised to power 1 / n which is four. So
minus one. So let's divide by 20,000.
then raised to power 1 / 4 that's like
raised to power.25
that gives 1.13
which is the same thing as 11.03%.
Can see the two formulas give us the
same answer. Yeah.
And that is why I'll prefer this
approach because with this approach two
regardless of your situation it will
give you the answer unlike approach one
that will only give you the right answer
only when CO is the same as your
investment rate. Now let's work a
question whereby the
the
investment rate is different from
financing rate. Then that will add a
proper spice to what we're talking
about. So look at this investment. Yeah,
you have year zero
um year 1 cash flow, year two, year
three, year four and year five. So year
0 let's say remains 20,000 outflow.
That is the net for year 1. For year 0,
year 1 there's inflow of 4,000.
Year two there's net outflow.
Year three, another inflow of 6,000.
Year four, 7,600.
Let's say 10,000 here. So, let's work
with this. Remember the first thing is
you need to know your reinvestment rate.
So, let's say the question has given
reinvestment rate
at 6%.
and financing rate which means that's
at 9%.
And we need to calculate MIR. So you can see
see
all this cash flow 4,000 the inflow
6,000 that we made 7,600 we made we need
to reinvest it at 6%. Whereas all these
places where we needed money that we
spent money will
discount at 9%. Because our cost of
financing is 9%.
So which means we still need to apply
that formula which is this one
terminal value and present value of
outflows. So let's do the present value
of outflows first.
So for this one we know that our
discount rate discount factor
will be one at year zero. So the present
value remains 20,000
and this is another outflow but this can
factor will be different
because this is year two and it's still
going to be at 9%.
So this is at 9%. So we need to go to our
discounting table and look at 9% year 2
So that will be discounting factor at 0.842.
0.842.
And if I multiply 0.842
842 * 2000 that will give us the PV of
that outflow.
So we've gotten the PV of that outflow.
So for outflow we already know the total
is addition of these two and that will
give us 216 84.
84.
So we already know the PV of our
outflow. Now we need to know the
terminal value of our inflow.
Yeah, N is five as we can see. So what
we are left with now is the terminal
value of all the inflows. And from this
question we can see that we have four
inflows 4,000 6,000 this and this. So
which means we need to get the terminal
value for each of them. And terminal
value means we need to push forward
compounding at the reinvestment rate
because we're going to be investing it.
So this year 1 of 4,000 if we need to
reinvest it we we'll be reinvesting it
for how many years to be from year 1 to
year 2 year 3 that's 2 3 4 and likewise
like that. So for 4,000. So
So
so let's do terminal value. Let's do
like working one here. Terminal value of inflows.
So for year one where we have inflow of 4,000.
4,000.
We're going to multiply it by one 1 +
investment rate of 6%
and for 4 years. So that will give us 1.06
1.06
* 4,000
and that means for year one
inflow that we are getting by time we
invest it by the end of the investment
life of 5 years this money would have
For year two, we didn't make money. So,
we're going to jump and pass to year
three where we are making 6,000.
And we can reinvest it at same 6%
however only for 2 years.
So, if we calculate that 1.06 raised to
power 2
* 6,000
that gives us 6,741.6
six year four and year five. For year
five, remember this 10,000 we don't have
time to reinvest it because it's just
coming at the end. So that remains the
stamina value.
Easy 10,000 just like we did before. But
for year four, we have 7,600
that we can still reinvest
but only for one year. So that means we
have 1.06 * 7,600
and that gives 8,56.
So which means the total terminal value
of all our inflows is addition of all of
this. So I'm going to add that together.
that gives 29 847.5.
So which means we have the terminal value
value
of our inflows.
And once we have that then we can go
back to our formula that says that MR
is equals to terminal value of all the
inflows 29847
divide by the present value of outflow
and rais^ 1 / 5 - 1 so if I divide that
by 21 684
I have 1.376
raised to power 1 5
that gives 1.0
666 then -1 that goes to 0.066
That is MR for that question. Even if
you put it on Excel, like I said, I will
show you on Excel how to do it quickly.
So, just like I promised, I was going to
also show you how you can do this so
easily on Excel. Yeah, you can have it
in exam as well. So, you can compute on
Excel. So, you need to know how to do it
both manually and on Excel. So, you want
to do this on Excel, all you need to do
is to start with equals to. Remember any
formula on Excel needs to start with
equals to then you just put MR right
right
is already coming up but even if it's
not coming up type M then open a bracket
then highlight all the values that you
are trying to work with all the cash
flows all of them and you put a comma
then you put the finance rate for this
particular question remember we said we
will assume that the finance rate and
investment rate are similar. So this
finance rate now we put 8%.
And likewise the reinvestment rate we
put 8%. Close the bracket. Enter. Then
you have 11%. Remember when we did it as
well we had 11%. And that is for that
question the first question. The second
question as well these are the cash
flows that we plotted. We have the
investment rate at 6% financing rate at
9%. So if we use the same formula equals
same one I like all the cash flows
comma the first one is the financing
rate which is 9% comma reinvestment rate
then if you enter you have the MR in
percentage and that is it you can see 6.6%.
6.6%.
Which was exactly the same thing we got
when we did it manually. So that is MR
for you. Even IR you can also calculate
on Excel in case you are wondering if
it's possible. Yes, the same way
IR then I like all of this. So for this
particular investment that is your IR
for that investment. The same thing you
can do for this guy too. So this is MR
want to get the IR can also use the same
formula. Yeah. So everything that you
can calculate manually can calculate on
Excel. That is it. If you have any
question remember to always bring it up
and hope this is clear. So we're going
to move into the last part of this
measurement which is duration. Remember
for NPV IRRa and discounted payback
method I've referred you to my earlier
videos on FM. It's the same
understanding that you need to have.
Please go and revise those lectures 22
to lecture 25. Then some practice
questions also follow those lectures.
Then this one we've dealt with modified
IR. The next one I'm going to deal with
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