However, about the investment phase and return phase, I find it rather difficult to reason out the following items as detailed below:

1) tax savings to be treated as investment phase

2) the additional working capital for subsequent year, say after year zero i.e that is in year 1, such additional working capital is to be treated as return phase.

To be honest it is slightly arguable.
However, as far as your examiner is concerned, the investment phase is simply the original investment (when the net cash flows are negative) and the return phase is all the later flows.
In P4, the cash flows will be relatively simple when MIRR is required i.e. negative at time 0 (and possibly time 1 if the investment is payable over 2 years, but less likely) – this forms the investment phase. All the later net flows are treated as the return phase.

Thank you for your explanation. It has indeed helped me to understand your lecture better now which has unveiled so many points which I have never thought to have overlooked or misunderstood them.

sorry to come back on this. However how can there be more than 1 IRR?

So the MIRR solves that issue as well as the issue of the restriction on the investment amounts (as per previous lecture with Project A @15% and B @18%)…..I am still a little confused as to how the MIRR solves this.

The fact that there can be more than one IRR is revision from F2 and F9 (although you would never be expected to deal with it – just to be aware that it can happen). Every time there is a change in the sign of the cash flows (positive to negative and vice versa) there is potentially (but not always) one more IRR.

MIRR treats the flows as though they are reinvested at the cost of capital and therefore always leads to the same conclusion as NPV when choosing between investments. IRR treats the flows as though they are reinvested at the IRR and can therefore lead to different conclusions than NPV when choosing between investments.

You have mentioned that MIRR is almost always less than IRR. This is logical as MIRR assumes investment at cost of capital which is less than IRR for positive/acceptable projects.

Is it possible for MIRR to be more than IRR? hypothetically I can only think of a case when cost of capital is more than IRR. This is the only case when MIRR can be more than IRR, right?

Additionally, I suppose the case when IRR is less than Cost of Capital and MIRR is more than capital can never happen right? because if Mirr is more than cost of capital it means that (PVr/PV1)^1/n must be >=1 and this can only happen when PVr is more than PV1 which itself implies that project has NPV>=0 which subsequently means that IRR>=cost of capital. Please confirm if my understanding is correct.

the initial working capital requirement in year zero will fall under the investment phase, so will the subsequent working capital requirements be under the same investment phase or return phase? thank you in advance,

I think that if they do occur, then best for the exam is to treat them as part of the return phase (although I am sure that if they were relevant then the examiner would allow it either way).

Sir,
As we know working capital requirements in subsequent years can change in either way as increase or reduction, what if increase in working capital(outflow ) is considered part of investment phase and decrease in WC as return phase. Will this approach be acceptable or is it plain wrong?

What if the tax payable/refundable is on arrears basis, in which case, in this example, these cash flows will fall into the 6th year. Is the life of the project then 5 years or 6 years?

I have a query:
What if any of the cash flows are negative? So you will have the initial investment and then cash inflows over the years. Say for example, Year 2 makes a negative cash flow, then will that cash flow be considered in PV of return or investment?

Dannyboy says

Dear sir,

You mentioned in your earlier lecture that there can be more than one IRR and that one cannot compare projects using IRR.

My question is how did MIRR solved this problem if it ever did.

Please enlighten me with this.

Tq

John Moffat says

There will only be one MIRR, and also the project with the higher MIRR will always also be the one with the highest NPV.

Dannyboy says

Dear sir,

Thank you for the very splendidly tactful reply.

However, about the investment phase and return phase, I find it rather difficult to reason out the following items as detailed below:

1) tax savings to be treated as investment phase

2) the additional working capital for subsequent year, say after year zero i.e that is in year 1, such additional working capital is to be treated as return phase.

Please enlighten me on this.

Tq in advance.

John Moffat says

To be honest it is slightly arguable.

However, as far as your examiner is concerned, the investment phase is simply the original investment (when the net cash flows are negative) and the return phase is all the later flows.

In P4, the cash flows will be relatively simple when MIRR is required i.e. negative at time 0 (and possibly time 1 if the investment is payable over 2 years, but less likely) – this forms the investment phase. All the later net flows are treated as the return phase.

Dannyboy says

Dear sir,

Thank you for your explanation. It has indeed helped me to understand your lecture better now which has unveiled so many points which I have never thought to have overlooked or misunderstood them.

Tq

John Moffat says

You are welcome 🙂

rouquinblanc says

sorry to come back on this. However how can there be more than 1 IRR?

So the MIRR solves that issue as well as the issue of the restriction on the investment amounts (as per previous lecture with Project A @15% and B @18%)…..I am still a little confused as to how the MIRR solves this.

Thank you

John Moffat says

The fact that there can be more than one IRR is revision from F2 and F9 (although you would never be expected to deal with it – just to be aware that it can happen). Every time there is a change in the sign of the cash flows (positive to negative and vice versa) there is potentially (but not always) one more IRR.

MIRR treats the flows as though they are reinvested at the cost of capital and therefore always leads to the same conclusion as NPV when choosing between investments. IRR treats the flows as though they are reinvested at the IRR and can therefore lead to different conclusions than NPV when choosing between investments.

anka1991 says

Dear John,

You have mentioned that MIRR is almost always less than IRR. This is logical as MIRR assumes investment at cost of capital which is less than IRR for positive/acceptable projects.

Is it possible for MIRR to be more than IRR? hypothetically I can only think of a case when cost of capital is more than IRR. This is the only case when MIRR can be more than IRR, right?

Additionally, I suppose the case when IRR is less than Cost of Capital and MIRR is more than capital can never happen right? because if Mirr is more than cost of capital it means that (PVr/PV1)^1/n must be >=1 and this can only happen when PVr is more than PV1 which itself implies that project has NPV>=0 which subsequently means that IRR>=cost of capital. Please confirm if my understanding is correct.

Thank you for amazing lectures!

John Moffat says

Yes – your understanding is completely correct 🙂

Fatma says

the initial working capital requirement in year zero will fall under the investment phase, so will the subsequent working capital requirements be under the same investment phase or return phase? thank you in advance,

John Moffat says

That is a very good question 🙂

I think that if they do occur, then best for the exam is to treat them as part of the return phase (although I am sure that if they were relevant then the examiner would allow it either way).

sohail says

Sir,

As we know working capital requirements in subsequent years can change in either way as increase or reduction, what if increase in working capital(outflow ) is considered part of investment phase and decrease in WC as return phase. Will this approach be acceptable or is it plain wrong?

John Moffat says

I have answered this in my previous reply.

Fatma says

Thanks a lot

John Moffat says

You are welcome 🙂

Fatma says

When you are calculating the net cash flows, where will the tax savings on capital allowances be considered in the investment phase or return phase?

John Moffat says

Hi Fatma

They will be treated as part of the investment phase.

tinashe says

well explained!

garygood says

What if the tax payable/refundable is on arrears basis, in which case, in this example, these cash flows will fall into the 6th year. Is the life of the project then 5 years or 6 years?

John Moffat says

Six years.

garygood says

Many thanks.

nzilani says

great and very helpful. very easy to understand and excellently explained

sahil107 says

I have a query:

What if any of the cash flows are negative? So you will have the initial investment and then cash inflows over the years. Say for example, Year 2 makes a negative cash flow, then will that cash flow be considered in PV of return or investment?

miqbalk says

very good and helpful

osru says

thank you. well explained and easy to understand.