Is the Modified Internal Rate of Return (MIRR) the maximum rate at which the cash outflows for an investment project can be financed? For instance, if a project costs $2,000, has a MIRR of 12%, a cost of capital of 10%, and the present value of cash inflows is $2,300, does the MIRR represent the highest rate at which the initial $2,000 investment can be borrowed or financed so that the reinvestment of cash inflows from the project at the cost of capital will not exceed the cost of financing? In simpler terms, does borrowing $2,000 at the MIRR rate equate to the cash inflows being reinvested at the cost of capital over the project’s duration? (Figures are for representation only)

Simply saying, is $2000 borrowed at MIRR over project life = $2300 reinvested at 10% over the life of the project ?

in example 3 you illustrated that MIRR can be used to compare different projects i.e. by choosing the one with Higher MIRR. However, I still think it is misleading to use MIRR to compare different projects because it a relative measure and not absolute measure. for example project with lower MIRR may give us high NPV.

You can (although in the exam, when it has been asked it has just been to do the calculation. You haven’t actually been asked to do anything with it 馃檪 )

Sir but I want to understand why鈥檚 there a need to reinvest cash receipts(whether at cost of capital or IRR) earned from the project, in the first place?

It is not that there is a need. It is just that if the IRR is used to choose between two projects then it is only valid to automatically choose the one with the higher IRR if we assume that the returns are reinvested at the IRR.

You are right when you say 2000 is the PV of the Investment Phase. Now if you see the formula of MIRR in the notes or as Sir wrote down on the board in the lecture, 2000 will come in denominator only.

We are dividing PV of return phase (which is 2257) by PV of investment Phase (which is 2000).

By definition, the IRR is the rate of interest at which the NPV of the project is zero.

It is rarely used in exams to appraise projects – we usually calculate the NPV. However if the IRR is more than the cost of capital then the NPV will be positive and we will accept the project. If the IRR is less than the cost of capital then the NPV will be negative and we will reject the project. (For more, watch the Paper MA and FM lectures on the IRR, because this is revision of MA and FM).

However there are problems using the IRR (which is why it is rarely asked for in the exam). MIRR is introduced in Paper AFM because it does in a sense deal with the problems, as I explain in the lecture.

Hello, when comparing two projects, agreed we consider the IRR, then we consider how long the return is, in the example, one project is 10% over 15 years while the other is 12% over 2 years, before considering the re-investment of the receipts at IRR, should we not also consider the advantage of the pay back period of each of the projects. Specifically in a scenario which details capital rationing.

In practice, companies would look at a range of measures and then form an overall judgement. In the exam, if choosing between projects we us the NPV criteria. IRR’s are irrelevant in the exam (apart from discussion) unless you are specifically asked to calculate them, and, of course, if you are asked to calculate them then you would probably be asked to calculate the MIRR as well (although both IRR and MIRR are not asked often). Whether or not it is capital rationing makes no difference to my last paragraph 馃檪

Both formula give the same result, but since the formula given on the formula sheet is the one that I work through in the lecture, it is rather silly to use the other one!

The terminal value is the value at the end of the project and is arrived at by compounding (i.e. adding on the interest) as opposed to the present value, which is arrived at by discounting (i.e. removing the interest)). Terminal values are not asked in Paper AFM, but if they interest you then watch the Paper F2 lectures on interest, where they are explained – they can be asked in Paper F2.

mkchimbganda says

Thank you. Is it okay to use excel formulas for NPV, IRR and MIRR?

John Moffat says

Yes – you should use the excel formulae 馃檪

mkchimbganda says

Thank you !! 馃檪

Akhil004 says

Hi John,

Is the Modified Internal Rate of Return (MIRR) the maximum rate at which the cash outflows for an investment project can be financed? For instance, if a project costs $2,000, has a MIRR of 12%, a cost of capital of 10%, and the present value of cash inflows is $2,300, does the MIRR represent the highest rate at which the initial $2,000 investment can be borrowed or financed so that the reinvestment of cash inflows from the project at the cost of capital will not exceed the cost of financing? In simpler terms, does borrowing $2,000 at the MIRR rate equate to the cash inflows being reinvested at the cost of capital over the project’s duration? (Figures are for representation only)

Simply saying, is $2000 borrowed at MIRR over project life = $2300 reinvested at 10% over the life of the project ?

John Moffat says

Effectively what you are saying is correct 馃檪

Akhil004 says

Thanks for the reply ??

abokor says

Hello, hope u are keeping well.

in example 3 you illustrated that MIRR can be used to compare different projects i.e. by choosing the one with Higher MIRR.

However, I still think it is misleading to use MIRR to compare different projects because it a relative measure and not absolute measure. for example project with lower MIRR may give us high NPV.

Hope u have got my point.

John Moffat says

The one with the highest MIRR will always be the one that also has the highest NPV (which is not the case with the IRR).

Having said that, as I say in the lecture it is really a bit of a cheat (which is why it isn’t asked often, although certainly can be asked).

abokor says

Thanks for the quick and concise explanation.

For further clarification, can we use MIRR to compare projects of different sizes.

John Moffat says

You can (although in the exam, when it has been asked it has just been to do the calculation. You haven’t actually been asked to do anything with it 馃檪 )

abokor says

Got it.

Thank u very much sir

John Moffat says

You are welcome.

Noah098 says

Sir but I want to understand why鈥檚 there a need to reinvest cash receipts(whether at cost of capital or IRR) earned from the project, in the first place?

John Moffat says

It is not that there is a need. It is just that if the IRR is used to choose between two projects then it is only valid to automatically choose the one with the higher IRR if we assume that the returns are reinvested at the IRR.

manavarya says

Hello,

PV of Investment Phase was calculated as 2000, then why did you take it in denominator while calculating MIRR?

Please explain.

Thank You

shanky95 says

Hi Manavarya!

You are right when you say 2000 is the PV of the Investment Phase. Now if you see the formula of MIRR in the notes or as Sir wrote down on the board in the lecture, 2000 will come in denominator only.

We are dividing PV of return phase (which is 2257) by PV of investment Phase (which is 2000).

Hope I was able to explain.

Thanks

John Moffat says

Thank you Shanky95 馃檪

hallesheron says

please Sir what does the Internal rate of return (IRR) actually calculate

And how do you choose if to go ahead with a project or not when using IRR?

John Moffat says

By definition, the IRR is the rate of interest at which the NPV of the project is zero.

It is rarely used in exams to appraise projects – we usually calculate the NPV. However if the IRR is more than the cost of capital then the NPV will be positive and we will accept the project. If the IRR is less than the cost of capital then the NPV will be negative and we will reject the project.

(For more, watch the Paper MA and FM lectures on the IRR, because this is revision of MA and FM).

However there are problems using the IRR (which is why it is rarely asked for in the exam). MIRR is introduced in Paper AFM because it does in a sense deal with the problems, as I explain in the lecture.

herafatima says

Hello, when comparing two projects, agreed we consider the IRR, then we consider how long the return is, in the example, one project is 10% over 15 years while the other is 12% over 2 years, before considering the re-investment of the receipts at IRR, should we not also consider the advantage of the pay back period of each of the projects. Specifically in a scenario which details capital rationing.

John Moffat says

In practice, companies would look at a range of measures and then form an overall judgement.

In the exam, if choosing between projects we us the NPV criteria. IRR’s are irrelevant in the exam (apart from discussion) unless you are specifically asked to calculate them, and, of course, if you are asked to calculate them then you would probably be asked to calculate the MIRR as well (although both IRR and MIRR are not asked often).

Whether or not it is capital rationing makes no difference to my last paragraph 馃檪

herafatima says

Thanks.

John Moffat says

You are welcome 馃檪

Ernest says

Thanks very much. This very clear to me now.

But please is that formula different from this one Terminal Value of Returns(Future Value)/PV of Investment^1/n -1

Will both turn out the same answer and what is the terminal value?

John Moffat says

Both formula give the same result, but since the formula given on the formula sheet is the one that I work through in the lecture, it is rather silly to use the other one!

The terminal value is the value at the end of the project and is arrived at by compounding (i.e. adding on the interest) as opposed to the present value, which is arrived at by discounting (i.e. removing the interest)).

Terminal values are not asked in Paper AFM, but if they interest you then watch the Paper F2 lectures on interest, where they are explained – they can be asked in Paper F2.

Ernest says

Thank you very much. Well explained!

John Moffat says

Thank you for your comment 馃檪

Collins says

Why is the working capital not included in the investment phase?

John Moffat says

It is included!! The 2,000,000 includes the 200,000 working capital.

Have you watched the previous lecture as well?