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ACCA AFM | Investment Appraisal | Advanced Techniques | Modified IRR | MIRR | Lecture 7

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Summary

Core Theme

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

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

8,000 * 9259

that gives 7 4 07 12,000

12,000

multiply by85 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

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 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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คำบรรยาย YouTube:ACCA AFM | Investment Appraisal | Advanced Techniques | Modified IRR | MIRR | Lecture 7