IRR Series Part 1: Introduction

Welcome to the first of a five-part series on the Internal Rate of Return! This is an advanced topic and I’m pleased to teach it to you. It is fairly theory-heavy and it’s going to take five whole posts and a heck of a lot of words, so strap in, get your cup of caffeine, and lets get right to it –

Yes, there will be maths

A terrible choice

No, I’m not talking about the choice you made to read this. For the five people who are left after that rousing introduction, let me ask you what you would rather do in the following scenario. Your cousin Bobby comes up to you and asks for some money. “It’s a loan, ” he pleads, ” only one-hundred dollars. I’ll pay you back. You know I’m good for it.” Those words strike fear into any relative, and for good reason: Bobby has lived from job to job, spending faster than he can make money. Probably has a bunch of credit card debt. What could be so important that he needs $100 and only $100 for? Your aunt, his mother, was very kind to you growing up. She’s passed now and you feel this irrational need to help Bobby out. He gives you two options:

  1. You pay Bobby $100 now and he pays you back $10 for the next ten years and gives the $100 back at the end
  2. You pay Bobby $100 now and he pays you back $20 for the next five years and gives the $100 back at the end

Knowing you feel compelled to make a loan, which one would you take? A no-brainer, right. You want to have the money back as soon as possible. Option 2 is your decision. Either way you get back your $100, so why is #2 better?

You get it back faster?

Right. You want that money back faster. It’s just an innate thing that we all understand and it doesn’t take economic theory. That money you get back sooner is worth more to you now than it would be later.

The Time Value of Money

The money in your hand now is worth more than it will be in the future. Bobby’s $10 each year over ten years equals $200 ($100 plus the $100 he pays you back at the end), same as $20 over five years, but it has less innate value to you over ten years. There must be some way to compare the two. If you are going to get paid, it is better to get it now. How much better? I’ve got you covered. In part 2 of the IRR Series.

What we will need to be able to do is to take that $200, accounting for how we got it back (how much each pay period), and work backward to today. We then can generate a value that the $200 we will get back is worth to us today. This is handy for comparing both deals.


The problem is, this is Bobby. Irresponsible, erratic, untrustworthy Bobby. You are fully aware he might fail to pay you back, instead paying you with ridiculous excuses. There are, of course, a lot of variables going into this, not the least of which, that he is family. You might even be able to work out a probability each year that he fails to pays you the $20.

Say you think cousin Bobby has a 20% probability each year that he will fail to pay you back what he owes you that year. He offers you deal #2 ($20 per year for five years). His sister Sally, who is also unreliable, but nowhere near as bad as Bobby also wants a $100 loan but is willing to pay it back over ten years, $10 per year (scenario 1). You think that Sally has a 5% probability of not paying you back each year. Which deal should you take? Bobby pays you back more quickly, so the money is worth more, but there is more risk. Vice versa for Sally. There has got to be a way to mathematically work back to a value in today’s dollars.

Each deal you consider might have a different risk. You need to be able to calculate a value that is used to decrease the value of the money you receive later as a result of the risk you take. I’ll teach you that in part 3.

Net Present Value

Once you have an idea about the risk you can take the cost of the investment (or loan) you make, plus the annual income that it makes, plus any amount you make at the end of the deal (in real estate this would be selling the property) and work back to find what all those returns are worth to you in today’s dollars. That is the Net Present Value (NPV). We’ll talk about that in part 4.

The Internal Rate of Return

Let’s change our scenarios slightly:

  1. Sally would like $100 and will pay you back $20 per year for five years and then pay you $100 at the end. She has a risk of 5% of not paying you each year.
  2. Sandy (your third cousin) would like $100,000 and will pay you back $20,000 each year for ten years. She will then pay you back $100,000 at the end. She has the same risk of 5%.

Same scenario, except Sandy wants 1000 times more. Yikes! Which is better?

Simply trying to work back to the value of the deal in today’s dollars won’t be able to give you a comparison of each deal. Don’t worry about the math, but it turns out Sally’s NPV ($58.30) is much lower than Sally’s ($107,526.31). Hers was much higher in large part due to the greater magnitude of the deal amount (1000x more loaned).

These examples are intentionally made to be very different but the deals you might do will have more subtle differences. If the amount of initial investment or the annual income on them are different, just calculating an NPV won’t help you compare. Sally netted you 50 odd bucks but you only had to put up $100. It cost a lot more for Sandy’s deal but it’s worth a lot more. Wouldn’t it be nice if there was a way to normalize each deal?

What if we could calculate a risk that would make both NPV values be equal? Any risk that was higher than that would be too much, causing us a loss (and we wouldn’t take the deal). Any risk lower would give us a gain. This risk percentage would set NPV to zero (meaning the deal didn’t make us any money or lose us any money). Then we could benchmark all our deals to this and compare them. That risk value is the IRR.

If I lost you there, no problem. That’s why there are 4 more posts coming at you like a freight train.

Yes, I know. It’s a passenger train.

See you next week.

Dr. Equity