Internal Rate of Return by definition is the rate of return at which the Net Present Value of a stream of payments/incomes is equal to zero.

As you know, money devalues over time. The rate at which it does is commonly referred to as the "discount rate". Therefore, let's say you have an payment/income profile as shown below and we assume a discount rate of 7%. If you take the difference between the net present value of the payments and the net present value of the returns, you get the net present value of the investment. In the case shown below that turns out to be $70,000 - $68,755.45 = $1,244.55.

Investment Return Year 0 $70,000 --- Year 1 $12,000 Year 2 $15,000 Year 3 $18,000 Year 4 $21,000 Year 5 $26,000 ------------------------- NPV (Year 0) $70,000 $68,755.45Now the question is: at what discount rate would the net present value of my investment be zero? In other words, at what rate would money have to devalue at in order to make my investment (i.e., payments vs. income) worth nothing in net present value terms. In the case shown below, that discount rate would be 8.66% and therefore, 8.66% is the Internal Rate of Return for the above described payment/income stream.

Now the next question is: so why is this important? Well, it is important because you have now learned that if money devalues at 8.66% you make nothing on your investment. Ya, so what? Well, if you knew of a place where you could--without question--invest your money and get 8.66% return on your investment and you held on to your money and didn't invest it, then your money would be devaluing at a rate of 8.66% regardless of the going market discount rate.

Now, if you chose to not invest your money in the place that would earn you 8.66% return because you knew of another place that would earn you 10.24% return (without question), then you'd be acting very prudently, no! Yes! And that is why comparing Internal Rates of Return is a good way to decide where to invest your money. The investment with a higher Internal Rate of Return is USUALLY the bettern investment.

Usually, why only usually? Well, because of uncertainty. As Harry Parker pointed out earlier in another message, there is often uncertainty associated with the Internal Rate of Return quoted to you by a business or mutual fund. Whereas, in the case of a CD the uncertainty is practically non-existant.

As long as the investment is irreversible and you have the ability to delay your decision, uncertainty creates "option value" (see Avinash Dixit and Robert S. Pindyck, "Investment Under Uncertainty", Princeton University Press, 1994 for the full blown version and "The Options Approach to Capital Investment" by the same authors in May-June 1995 Harvard Business Review for the digested version).

For example, let's say you had two different investment opportunities. The first had an IRR of 9.67% with question, guaranteed! The second had a projected IRR of 9.67% with a chance that it could be lower or higher depending on how the wind blows (couldn't resist the AE pun). Well, you could do a couple of things. You could invest in the sure thing 9.67% investment or your could wait and see what happens to the IRR for the second investment and then decide what to do? If you wait, you're excercising your option value. If you don't wait, your cashing in your option value.

I really encourage you to read up more on "option value" and its impact on investment decisions. The orthodox method of making investment decisions (i.e., if NPV > 0 then invest, which is basically what I discussed at the outset of this message) can often lead you to make imprudent investment decisions. Anyway, good luck.

Hope this helped.

S. Yousef Hashimi

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Subject: Internal Rate of Return

This has nothing directly to do with energy, but I need help and there are a lot of well informed people in the bioenergy forum. So I will start with the best.

What is the significance of 'Internal Rate of Return'?

If you can invest $100,000.00 in a 10 year CD at 10% or invest $100,000.00 in a business that has zero cash flow for the first two years; that produces a 10% Internal Rate of Return over a 10 year period ------ Either

Thanks

Don Jacobs, Sr. V.P. Energy Associates of Hawaii, Inc. | In the business of 15-2722 Popaa Street | establishing a biomass Pahoa, HI 96778 | to fuel ethanol production (808) 965-0361 | facility in Hawaii. donj@aloha.net