Using IRR as profit criteria, with an upward sloping NPV curve.

Hi,

Using the profit criteria suggested by the code reading, the profit criteria should be defined as - accept the profit if: IRR > cost of capital, says 4%.

Suppose the NPV function of a project is 100-1.05 / (1+i)
The internal rate of return – IRR – is 5%.

IRR = 5% > COC = 4%, thus we accept the project.


Since the NPV function is upward sloping, using any discount rate lower than 5% must product a negative NPV.

Hence, if we use a discount rate equal to the cost of capital (4%), then I would produce a negative NPV = -0.96.

Using as our profit criteria, we reject the project.




I have 2 questions.

Question1:
Which profit criteria should I follow? IRR or NPV?

Question2:
Should I define the IRR profit criteria as
Accept the profit if : cost of capital > IRR

Then, if the cost of capital is 6%, we have a NPV of 0.94.
Both IRR and NPV criteria are past, but the project can’t product a return required by shareholder.

 

I think you've picked an unusual 'project': one that pays 100 now but that you have to pay back 105 for in the future. Others might call it 'borrowing'.

If it's the other way round, i.e. invest your 100 now for a gain of 105 in the future, NPV = -100 + 105/(1+i) = +0.96 at i=4%. And the IRR is greater than your cost of capital. In this case, you would invest (based on these criteria).

'Projects' normally involve some up-front investment: you're looking for something to invest in. However, given the unusual shape of the project you have suggested, which effectively involves you borrowing at a rate of 5%, then you're right: don't do it, since your cost of capital is less than the cost of this borrowing.

I think that consideration of the IRR is only going to work for more normal project shapes, i.e. where you invest now for future returns. Where the cash flows are more complicated, you could anyway end up with a number of roots to your IRR equation. You're generally safer to calculate the NPV.

 

thank you very much alpha9

could you please explain why the IRR is also the return offered?

I understand how to show that mathematically, but I can't explain in text

 

Not quite sure what you mean: IRR = internal rate of return by definition!

 

yes, I agree with you - IRR = internal rate of return

I guess that the acted note implies IRR = return acheived, because of the following 2 sentence in the acted note

(1)
The method has the benefit of highlighting the return achieved by the project.

(2)
One main advantage of the IRR is that provides a rate of return for the project.

*** i am using the 2007 acted note

 

Yes the IRR is the rate earned on an investment, if it is a "regular" investment with initial outflow and later inflow.

It is also the effective rate of borrowing if you are borrowing. Think of it as the other side of the investment above.

It is the return earned since, investing in a "bank account" that earns/charges the IRR and withdrawing/depositing the same cashflows, will result in the same final amount (last withdrawal/depost).

 

hi, what does the "regular" investment imply?

 

"Regular" in this context mean the "normal", "usual" type of investment project, ie Big initial outflow (payment) at start, possibly followed by other outflows, and which are all themselves followed by net inflow.

Borrowing would be the reverse of this.
And there are possibly other more complex cashflow profiles, some of which may have many (numerical) solutions for the IRR, or possibly even no real ones. These "non-regular" ones shouldn't be cause for concern in the exam.