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The value of NPV is taken in the IRR calculation, not the the values of individual cash flows, and that NPV could be positive or negative so how does it result in two IRRs unless we discount the same cash flows at different rates more than twice?
Suppose you had a project with the following cash flows:
0 (11,000)
1 7,500
2 7,500
3. 7,500
4. 7,500
5. (20,000)Initially we are investing, and getting inflows, however we are then effectively borrowing and having to repay at time 5.
If you calculate the NPV at various rates of interest and draw the graph (as I explain in my free lectures) you will find that the NPV starts negative, then becomes positive, and then becomes negative again as the interest rate increases. It crosses the axis twice and so there are two IRR’s (the IRR is the interest rate at which the NPV is zero).
Try it yourself for the following interest rates: 0%, 10%, 20%, 30% and 40% and you will see what I mean. The curve crosses the axis at about 5.6% and about 28% – there are two IRR’s.
Whenever there is a change in sign in the cash flows, there is potentially (but not always) one more IRR. In the example above there are two changes of sign and therefore potentially two IRR’s.
You will not be expected to calculate the IRR’s in the exam in this situation, but you are expected to know that the problem can exist.
Thank you.
Last question I promise. I understand all that but how are unconventional cash flows an indication of two different IRRs in the first place since individual cash flows don’t matter and only the NPV does?
Secondly, are you saying that interest rates don’t stay constant during the project life and may increase as a result of more borrowing at later stage?
By definition, the IRR is the rate of interest at which the NPV is zero.
Normally there is only one IRR and if the IRR is more than the cost of capital then we accept (because the NPV will be positive) and if the IRR is less than the cost of capital then we reject (because the NPV will be negative). So we can use the IRR to decide whether to accept or reject a project (but rarely in the exam – we just calculate the NPV at the cost of capital).
If there are changes of sign in the cash flows (as in the previous example I gave you) then there can be more that one IRR. This is a problem with using the IRR to decide whether to accept or reject because you can’t compare two (or more) IRR’s with the cost of capital.
(Although as I wrote before, you will not be expected to calculate multiple IRR’s in the exam, but you could just be expected to know the problem multiple IRR’s present).Have you watched my free lectures on this? The lectures are a complete free course for Paper FM and cover everything needed to be able to pass the exam well.
It seems that you might be learning the calculation of the IRR as a formula. If so then you do not need a formula (and it is not given in the exam). If needed watch my Paper MA (was F2) lecture on investment appraisal, because this is revision from Paper MA.
Hi John,
From your answers I understand that you are very familiar with the the cost-benefit analysis:
• net present value (NPV);
• profitability index (PI);
• financial internal rate of return (IRR).I need some help if you are available?
I want to understand how to to calculate all of this for some investment projects. Could you be so kind to help me with some practical example.
Basic examples to understand step by step.Thank you for your time. Appreciate all your support.
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