Elementary IRR Question

[Julie N.]

I told myself I wanted to have a firm grasp on IRR and have been researching online. I feel like it's easy to over complicate this and I've confused myself unfortunately :)..

The definition of IRR being the discount rate that makes NPV equal to 0 makes sense to me. The concept of NPV and discounting cash flows makes sense to me. What I don't understand is when IRR is referred to as a compounding annual rate of return.

I read this example and it threw me off.. "Abel sells land for $20,000 that he bought 4 years earlier for $10,000. The internal rate of return was 19%. That is the annual rate which compound interest much be paid for $10,000 to become $20,000 in 4 years"  

What about a scenario with multiple cash flows? For instance with an investment then with 5 years cash flows yielding 26.9% IRR.

($957,900)

,

$87,964,

$112,892,

$131,070,

$119,800,

$2,336,368,

26.95576%

Shouldn't you in principal be able to compound $957k annually by 26.9% and arrive at the same total amount as the total of the cash flows received over the hold? In the example above I know I am missing something as the total of the cash flows is $2.788M vs the simple compound interest of $957,900 over 5 years at 26.9557% is $3.159m.

Thanks for helping me clear this up!

[Brian Burke]

Simple answer, @Julie N.!

In your compounding example, you are assuming that all of the earnings remain in the investment, meaning they compound each year at the same annual growth rate as the principal.  This would be true in a savings account where you took no withdrawals, for example.

IRR, on the other hand, measures cash flows. So in your IRR example you are showing cash flow every year, which means that money is distributed to you and there is no compounding on the distributed dollars because they are no longer in the investment.

If you run your IRR calculation like this (the same way you are using your compounding example), the IRR would be 23.8219%. Same dollars in, same dollars out, different timing.

-957,900, 0, 0, 0, 0, $2,788,094 = 23.8219% IRR

Or, you could run it like you did in your compounding example, using the compounded earnings (more dollars out, same % IRR as the % compounded):

-957,900, 0, 0, 0, 0, $3,159,236 = 26.9557% IRR

The lesson here is that you need to re-invest your earnings, or accept that the same IRR will give you fewer dollars than a comparable fully-compounding investment if you get any cash flow. Probably a good trade-off because you might want to use that money for something else.