How do you define IRR, saying that at this rate NPV=0 doesn't offer any help

DexterOnline

DexterOnline

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IRR is suppose to tell an analyst the profit or loss incurred from an investment in terms of percentage rate

Thus when I read from almost any textbook on finance that IRR is suppose to be some interest rate at which the NPV - net present value is zero, that boggles my mind

I mean the idea of saying that discounted cost equal discounted benefits using the IRR as the discount rate

But the rate you may get by setting net present value to zero may be of little use

Surely we all know that when the number of cash flows exceed the count of five, then one must resort to using iterative methods to find the rate that sets NPV=0

But even when we have a IRR formula such as solving three sets of cash flows with a resulting polynomial of order 2, you would get two conflicting IRR solutions

These solutions may be both real positive numbers

These solutions may be both real negative numbers

These solutions may be one real negative number and one real positive number

Or both solutions may be complex numbers

Say for a set of cash flows, there exist two IRR solutions of 10% and 20% such as

-100, 230, -132

So did the investor really made 10% or 20% on this investment

The logical explanation you would give is that using either 10% or 20% the net present value comes to zero meaning the discounted costs are equal to discounted benefits

Well and good, but the question

Did the investor made or lost money from this investment

Wasn't this the question that IRR was suppose to provide an answer for

Please help me understand something I may have missed with this example illustration of fallacies of IRR
 
Basically what IRR says is you will break even at that interest rate. In your example you have
Pay $100 immediately
Receive $230 in one year
Pay $132 in two years.
Using your 10%, if you earn 10% on $100 money you paid immediately, you would have $121 at the end of two years.
If you borrowed $230 at 10% for one year at the end of the first year, you would owe $253 at the end of year two.
At the end of year two, settle up. You have $121 from your 100 investment but own $253, so the net is you owe $132. Pay it! You don't have your $100 anymore but you also don't have anything left to pay out of pocket for that $230 you borrowed.

In essence you have the use of $230 for a year (worth $23 at 10%) for a cost of $2 actual but, figuring the time value of money for your $100 'investment' at 10%, you broke even. So, yes you got 10% on your money.

EDIT: Oh, you say, but I paid out the $232 and don't have anything to show for it. Well, sure you do. You still have what the $230 you borrowed has made for you. For example, suppose you had invested it at 20%. So you paid out $100 two years ago and now have $397 but owe $253 so really have a net of $144. Something about leveraging?
 
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Whats the net amount the investor has in her pocket at the end of investment period?

Does the amount she has at maturity reflect an earnings of 10% or 20%?

Think of the negative amounts as deposits at a bank account and positive amounts as withdrawals.

What amount does she have when she closes the account.
 
Ishuda said:
EDIT: Oh, you say, but I paid out the $232 and don't have anything to show for it. Well, sure you do. You still have what the $230 you borrowed has made for you. For example, suppose you had invested it at 20%. So you paid out $100 two years ago and now have $397 but owe $253 so really have a net of $144. Something about leveraging?
Click to expand...

OK

Let me show you few other investments

-100, 50, 50

-100, 60, 40

-100, 30, 70

In all these investments, the net sum is 0 and so is the IRR of 0%

This one makes sense doesn't it, even though interest was earned in interim periods yet at maturity the investor got left with a duck thus the IRR of 0%

In the earlier example the net sum of investment is -2, leaving the investor short changed

Thus if for investments where the investor broke even and made no profits, the IRR is 0%

And the anomaly of IRR in earlier example that states investor made 10% or 20% whereas at maturity has nothing to show for it in terms of money
 
In my view there is something inherently wrong with how the IRR equation is defined as its solution gives conflicting solutions

Take some of these investments with two cash flows each

1, 1

-1, -1

In the first instance we received two dollar one at present and one a year from now

In the second instance we paid two dollar one at present and one a year from now

In each of these investments, the IRR turns out to be -200%

I mean if you gave out dollar each to someone without receiving anything back you lost twice the money
 
DexterOnline said:
...In the earlier example the net sum of investment is -2, leaving the investor short changed...
Click to expand...

As you mentioned before, for an initial investment/income with investments/incomes at the end of each period/beginning of next period, then the IRR has n solutions (some of which may be the same) for a total term of n+1 investments/payouts.

If you want to ignore the time value of money, then yes, you can say the net sum was -$2 out of pocket in the example. However, in the financial world (and elsewhere) the time value of money is not ignored. Nor is it ignored in the calculation of IRR. In this particular case, the borrowing of $230 for a year. If you hid that $250 in your mattress and paid it back at the end of the year, you still had to pay the $23 interest (at the 10% rate). If you look at a spread sheet, it would go something like
Beginning of year 1: $100 in bank earning 10%
End of year 1: $10 interest paid so $110 in bank earning interest.
Beginning of year 2: Borrow $230, stick it in mattress. Balance of money is $340 with $110 earning 10% interest.
End of year 2: $11 paid in interest on $110 so have $230 in mattress and $121 in bank for total of $351. End of contract, so settle up. Turn over $121 in bank and pay additional $132 out of the $230 I kept in mattress.

I have $98 left and I am $2 out of pocket total BUT ONLY BECAUSE I STUCK THE MONEY IN THE MATRESS. If I had used the money to make money, even as little as putting it into an account earning 0.8%, I wouldn't be out any money. How so some ever, calculation of IRR doesn't take things like that into account. That is why it is called an INTERNAL rate or return.
 
Hey, many thanks for the explanation

It seems one of my theories is not quite right

So let me go back to the research desk and do some more "thinking"

Thank you for being so kind and lighthearted unlike my mentor Sir Wilmer who threw the Bible at me

Hymns to The Lord

Hallelujah

Not sure what Lord would think of my current research to find His rate of return here at http://tadxl-addon.thinkanddone.com/
 
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